Estimation of the Z → νν background to New Physics searches in ATLAS Tanya Sandoval of Wolfson College University of Cambridge A dissertation submitted to the University of Cambridge for the degree of Doctor of Philosophy May 2012 ii iii Estimation of the Z → νν background to New Physics searches in ATLAS Tanya Sandoval Abstract This thesis describes a series of studies related to searches for new phe- nomena, beyond the Standard Model of particle physics, in high energy hadron collisions. In such searches, it becomes crucial to identify the Standard Model backgrounds in order to resolve a potential new signal. The thesis presents a method that uses photon events to determine one of such backgrounds, caused by the production of Z boson events. The studies performed to validate the method, both theoretically and experimentally, are presented and the method was shown to be successful as well as to provide reliable results. Theoretically, the method is found to be robust up to a ∼ 10% uncertainty. Experimentally, the method is implemented to estimate the Zνν + jets background for the SUSY 0`+ EmissT + jets search in the ATLAS experiment at the Large Hadron Collider, where this background is one of the most important compo- nents for the final sensitivity and is impossible to measure directly. The main experimental results presented are the latest from ATLAS at the time of writing, corresponding to the full dataset of proton-proton colli- sions delivered by the LHC in 2011 (∼ 4.7 fb−1) at √s = 7 TeV. Given that this method has been mainstream since 2010, brief comparisons to the results from previous analyses that used smaller datasets with the same √ s are also given, as well as additional cross-checks that support the robustness and validity of the method. The results presented here have contributed to the determination of the world’s best limits with respect to SUSY models, which currently exclude equal mass squarks and gluinos below 1.4 TeV. iv vDeclaration This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. This dissertation has not been submitted for another qualification to this or any other university and does not exceed the word limit for the respective Degree Committee. Tanya Sandoval vi vii Acknowledgements I would like to thank all those who have provided the support and guidance that has enabled me to complete this degree. In providing the financial support, I would like to thank the Mexican Science and Technology Council (CONACYT) and the University of Cambridge. Very specially, I would like to thank my supervisors: Andy Parker and Stefan Ask, without whom this thesis would not exist! Andy: thanks for always having faith on me in the first place, supervising me since the start of my PhD and enabling the opportunity to work in the ATLAS experiment and CERN – this has been an incredibly rewarding and memorable experience for me. Stefan: thanks for starting so many different projects with me, and for transmitting your enthusiasm and knowledge of the subject. Stefan started working with me on a project that was his idea, probably without knowing he was going to spend uncountable hours on a project that was my idea – this thesis! How to forget the winter night of 2010 at CERN, when our results were not making sense and yet we stayed trying to make them work, despite the snow storm outside and time – in the end, we didn’t get it on that day but rather after a couple of months! Thanks to James Stirling and Meg Shea for their collaboration to make my first journal publication happen; to TJ Khoo, without whom the best plots and sophistication in this thesis would not have been possible; to Nick Barlow, for teaching me how to fix segmentation faults, make nice plots and helping in my work for the ATLAS Silicon Tracker; to Chris Lester for making me believe in the importance of this project and not give up on it at the times when the results did not make sense; to Gareth Jones, for being always a personal tutor to me since my undergraduate studies at Imperial College. A big thanks also to the entire Cambridge High Energy Physics group and all the people at CERN who worked with me to make this project a reality. To my friends at Wolfson College, Cambridge and CERN, thanks for making my time there so much fun. Last but not least, I would like to deeply thank my parents Luz Maria and Jose Manuel, and my family and friends in Mexico, for their love and support; for always being there, making me laugh and cheering me up, especially during the most challenging times of my PhD. viii ix Preface Finding out how our Universe works has never been a bad idea. In fact, it is the quest for a deeper understanding of nature that has given us many of the things we now take for granted in modern life. The LHC, at present the world’s most powerful particle collider, has been built for this purpose – to answer some very profound questions about the nature of matter, and it is offering one of the closest possibilities for a ground-breaking discovery, as it has been deliberately designed to journey into uncharted waters, reaching energies in its particle collisions never achieved before in Earthly laboratories. For physicists like me, the main motivation lies in the incompleteness of our current best theory of particle physics: the Standard Model (SM). With its state-of-the-art technology, ATLAS, the world’s largest particle detector finally began taking LHC data in 2009 and with it, the searches for New Physics that can either complement or disprove the Standard Model. In the hype of the searches for new physics at all the LHC experiments, this thesis primarily concerns the presentation of a relatively new and sophisticated method (called here “ZfromGamma”) to estimate the amount of Z bosons which decay to neutrinos (Zνν) in data. In this case, Zνν is no longer considered a new process but rather a tarnisher of potential new signals. Moreover, the fact that neutrinos are involved in the final state, makes it one of the most challenging backgrounds to identify and quantify experimentally, for which the searches suffering the most from this background currently rely on its estimate. While based at CERN, I started this project in 2010 because at the time the SUSY searches had began analysing data and the primary concern then was how to resolve a potential new signal from all the particles we already knew; in other words, how to estimate the SM background. There was of course simulation (MC), but given that data/MC discrepancies had been found in some cases, in particular when modeling multi- jet events, which was one of the SUSY signatures searched for, the ultimate goal was to estimate all the backgrounds from data itself. On the other hand, at the time ATLAS as a detector was still being understood and calibrated, so when the first publications for new physics searches took place (between the end of 2010 and beginning of 2011), most based their background prediction on MC. After this however, the “era” of the data-driven methods for background estimation began and nowadays it is considered the default way to quantify a background, while MC is used only as a “cross-check”. xDuring this time, there was also the need to design a method to estimate a particular background which was unmeasurable in ATLAS: this was Zνν . Simultaneously, the other multi-purpose experiment at the LHC, CMS had already taken the initiative in designing such method, so this was another motivation for someone in ATLAS to take over this project. The enterprise was challenging: no such studies had been initiated in ATLAS before and so it was basically “starting from zero”. Indeed, the challenges became a reality and the project took a good amount of “trial and error” and dedication before it worked and looked the way it is presented in the following chapters – perhaps the thesis as a whole does not necessarily reflect that. Regarding the thesis structure, Part I starts with Chapter 1 where the presentation of the SM and the possibility for a new Beyond-the-Standard-Model (BSM) theory, called Supersymmetry (SUSY), to solve some of its problems are given. It is then explained why the precise estimation of SM backgrounds are an essential part of the search strategy in all BSM searches like SUSY. In addition, Chapter 2 provides the description of the experimental setup used based on ATLAS and the LHC. Part II starts with Chapter 3, where the motivations for a dedicated Zνν background study and the need of a method to estimate it are introduced. A method inspired from the possibility of using experimentally easier processes, of similar properties, is proposed, given that one process can be used to estimate the other if their relationship is well-known. Several key advantages and evidence, such as a guaranteed simple relationship with Z bosons, the possibility for large statistics and being data-driven given its clean signature in ATLAS, are given to justify the choice of a photon based sample as the experimentally easier process to estimate the Zνν background. With this, ZfromGamma is formally introduced as as promising method to estimate not just the Zνν background, but any other Z boson related background, as long as the Z/γ cross-section ratio (RZ/γ) is well-known. Though in principle, this is enough theoretically, experimentally additional corrections need to be considered, such as photon efficiencies, acceptance and purity. Therefore, the experimental method suggested is based on the idea of a control sample (here referred to as Control Region, CR) and the use of a Transfer Function (TF) to make the Z/γ conversion. Given the knowledge required of RZ/γ (not just at parton-level, but also at reconstruction level) for the method to be competitive in experiments, the dedicated theoretical studies performed are presented in Chapter 4 and, despite some variations observed, the overall theoretical uncertainty on RZ/γ is determined to be reducible up to 10%. With such positive outcome, the motivation to pursue the method experimentally in ATLAS followed and this work is presented in Chapter 5. The idea was to make ZfromGamma as data-driven as possible in order to free the results from as many theoretical uncertainties. The chosen xi search to test the method is the SUSY “0`” search, one of the searches with the highest SUSY-reach at the LHC and which relies on the prediction of the Zνν background, given its major contribution to the selected events where SUSY is searched for. The sections in Chapter 5 are hence dedicated to detailing the experimental framework and event selections implemented to define the photon-based control sample (CR1a), as well the procedures to determine the conversion factor - the Z/γ Transfer Function (TFZνν ). With the determination of TFZνν , the first main cross-check of the results is done by comparing the results directly against simulated Zνν data and indeed excellent agreement within the estimated uncertainties is found. The final section in this Chapter is then dedicated to showing the relevance of the ZfromGamma results to the chosen BSM search and how they were actually used, since a sophisticated procedure, based on a combined fit of all the background estimates, is implemented. In addition, the ZfromGamma results are also shown to be consistent with an alternative method based on a Z`` control sample (CR1b). Given the absence of a potential SUSY signal, the limits set by the 0` analysis are also discussed, as well as the impact of the ZfromGamma results on the SUSY mass reach. Lastly, Part III is Chapter 6, which gives the concluding remarks and outlook for both ZfromGamma and SUSY, a review of the latest results from CMS at the time of writing and the possible further improvements to the method. For ZfromGamma, perhaps the main conclusion is that the method demonstrated to be successful at estimating the Zνν background to new physics searches in ATLAS since 2010, and despite no signs of SUSY or other BSM physics found so far at the LHC, the searches continue and therefore, this method will remain crucial in determining if there are signs of new physics at all. The appendices mainly concern the presentation of past results, which were provided to the 0` analysis since 2010. With this, the reader can follow how the method evolved and improved with time, as well as realise the existence of other uses of the method other than for Z + jets background estimation. The last appendix lists the most common acronyms used throughout the thesis. xii Contents I. Foundation 3 1. Theoretical Background 5 1.1. Overview of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.1. Key features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.2. QCD at Hadron Colliders . . . . . . . . . . . . . . . . . . . . . . 11 1.1.3. Problems of the Standard Model . . . . . . . . . . . . . . . . . . 16 1.2. Overview of Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.2. The MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.3. Searches at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . 26 2. ATLAS and the LHC 33 2.1. The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.1.1. Operation Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.1.2. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2. The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.1. Coordinate System and Kinematic Variables . . . . . . . . . . . . 40 2.2.2. Detector Components . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2.3. Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.2.4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.2.5. Physics Object Definition . . . . . . . . . . . . . . . . . . . . . . 53 xiii xiv Contents II. Estimation of the Z → νν background to New Physics searches in ATLAS 59 3. Introduction 61 3.1. Calibrating physics processes via cross-section ratios . . . . . . . . . . . . 61 3.2. The challenging Zνν background . . . . . . . . . . . . . . . . . . . . . . . 63 3.3. Using γ events to calibrate Z boson normalisation . . . . . . . . . . . . . 64 3.4. ZfromGamma Method Overview . . . . . . . . . . . . . . . . . . . . . . . . 66 4. Theoretical Studies 71 4.1. The Z/γ Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2. V+jets production in leading–order perturbative QCD . . . . . . . . . . 73 4.3. Parton level analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3.1. V + 1 jet results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.3.2. Theoretical uncertainties . . . . . . . . . . . . . . . . . . . . . . . 78 4.3.3. V + 2, 3 jets results . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.4. Full event simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.1. Effects on the ratio . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4.2. Background estimate for a 0` SUSY search . . . . . . . . . . . . . 88 4.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5. Experimental Studies 95 5.1. Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.2. Event Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2.1. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2.2. Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.3. Inclusive Photon Sample (γ +X) . . . . . . . . . . . . . . . . . . . . . . 106 5.3.1. Object definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3.2. Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.3.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.3.4. Comparison with SM prompt photon results . . . . . . . . . . . . 111 Contents xv 5.4. Control Region Sample (CR1a) . . . . . . . . . . . . . . . . . . . . . . . 115 5.4.1. CR1a Object Definitions . . . . . . . . . . . . . . . . . . . . . . . 116 5.4.2. 0` Object Definitions and Event Selection . . . . . . . . . . . . . 118 5.4.3. Comparison with SM prompt photon results . . . . . . . . . . . . 123 5.4.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.5. Transfer Function (TFZνν ) . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.5.1. Efficiency and Acceptance . . . . . . . . . . . . . . . . . . . . . . 132 5.5.2. Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.5.3. Z/γ Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.5.4. Application of TF/ TF stand-alone estimate of Zνν + jets . . . . . 141 5.5.5. Summary of TF results and uncertainties . . . . . . . . . . . . . . 144 5.6. Context within the 0` analysis . . . . . . . . . . . . . . . . . . . . . . . . 146 5.6.1. Overview of relevant 0` results . . . . . . . . . . . . . . . . . . . . 146 5.6.2. Discussion: Comparisons with other CRs . . . . . . . . . . . . . . 156 5.6.3. 0` Interpretation and Limits . . . . . . . . . . . . . . . . . . . . . 161 III. Close 165 6. Conclusions & Outlook 167 6.1. ZfromGamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.1.1. CMS results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.1.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 6.2. SUSY and other BSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 A. Supplementary Moriond’12 results 177 A.1. Event displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 B. SMDP inclusive prompt photon cross-section measurement (35 pb−1)181 B.1. Photon Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 B.2. Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 B.3. Signal yield and Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 xvi Contents C. Results from Previous Analyses 191 C.1. Moriond’11 (35 pb−1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 C.1.1. Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 C.1.2. Event Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 C.1.3. Inclusive Photon Sample (γ +X) . . . . . . . . . . . . . . . . . . 194 C.1.4. Control Region Sample (CR1a) . . . . . . . . . . . . . . . . . . . 197 C.1.5. Transfer Function (TFZνν ) . . . . . . . . . . . . . . . . . . . . . . 202 C.1.6. Context within the 0` analysis . . . . . . . . . . . . . . . . . . . . 205 C.2. PLHC’11 (165 pb−1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 C.2.1. Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 C.2.2. Event Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 C.2.3. Inclusive Photon Sample (γ +X) . . . . . . . . . . . . . . . . . . 209 C.2.4. Control Region Sample (CR1a) . . . . . . . . . . . . . . . . . . . 209 C.2.5. Transfer Function (TFZνν ) . . . . . . . . . . . . . . . . . . . . . . 215 C.2.6. Context within the 0` analysis . . . . . . . . . . . . . . . . . . . . 219 C.3. EPS’11 (1.04 fb−1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 C.3.1. Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 C.3.2. Event Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 C.3.3. Inclusive Photon Sample (γ +X) . . . . . . . . . . . . . . . . . . 227 C.3.4. Control Region Sample (CR1a) . . . . . . . . . . . . . . . . . . . 227 C.3.5. Transfer Function (TFZνν ) . . . . . . . . . . . . . . . . . . . . . . 235 C.3.6. Context within the 0` analysis . . . . . . . . . . . . . . . . . . . . 236 D. Supplementary cross-checks on the method 243 D.1. TF stand-alone estimate of Zµµ + jets (Moriond’11) . . . . . . . . . . . . 243 D.2. γ + jets background in 0` SRs . . . . . . . . . . . . . . . . . . . . . . . . 245 D.2.1. The ‘LAr hole’ Example (EPS’11) . . . . . . . . . . . . . . . . . . 245 E. List of Acronyms 247 Bibliography 253 Contents xvii List of Figures 261 List of Tables 267 xviii “To my parents Luz Maria and Jose Manuel, and the memory of my brother Jose Manuel Jr. – thank you for everything.” 1 2 Part I. Foundation 3 Chapter 1. Theoretical Background The theoretical basis for the research performed in this thesis is the Standard Model – our current best theory of particle physics which has been successful at describing almost all experimental results to date, but that remains incomplete in the sense that several aspects are left unexplained or poorly understood. It is this ‘incompleteness’ and the possibility to find new physics at the present particle colliders which motivates the research in this thesis. The aim of this chapter is to summarise the theoretical background required to understand the contents in this thesis. Section 1.1 starts by outlining some key concepts of the Standard Model (SM), followed by a more specific subsection on Quantum Chromodynamics (QCD) applied to hadron colliders. The information for these parts was mainly extracted from references [1–4]. The section finishes by highlighting some of the current problems of the SM, despite its success, in order to motivate the search for new physics. The information for this part was mainly extracted from [5] to quote recent results. Section 1.2 then follows to introduce Supersymmetry (SUSY) - the theory chosen as a promising extension to the SM that could solve some of its problems, potentially at the energies of the Large Hadron Collider (LHC). The section starts by summarising the theoretical aspects of SUSY based on [5, 6], followed by the phenomenological aspects and current search strategy in ATLAS. Throughout this chapter, the reader is assumed to be familiar with some of the concepts and notation used in the references aforementioned. 5 6 Theoretical Background 1.1. Overview of the Standard Model 1.1.1. Key features Three of the four known fundamental forces in nature – the electromagnetic, weak and strong, which are thought to account for the dynamics of subatomic particles – are described by this simple model; simple because only a few of these particles appear to be fundamental. QFT - The model is formulated as a relativistic quantum field theory where particles represent excitations of spacetime fields and forces result from the exchange of the gauge bosons. All the dynamics, particle content and symmetries of the theory are described by a renormalisable Lagrangian (see below). The kinetic terms (quadratic in the fields) are associated to the propagators, while the other terms represent interaction vertices (conserved currents). Fermions are represented by spinor fields, gauge bosons by vector fields and the Higgs boson by a scalar field. Symmetry - The particles and interactions are partly the result of symmetry princi- ples. The symmetries of the theory are realised by transformations which leave the SM action invariant, leading to conserved current and charges (Noether’s theo- rem). Invariance under spacetime translations and rotations represent the global symmetries of the Poincare´ group, leading to conservation of energy-momentum and angular momentum; while invariance under gauge (phase) transformations represent the local symmetries of SU (3) × SU (2)L × U (1)Y – the SM group – leading to other conserved quantities like colour and electric charge. The three sub-groups represent the interactions due to the three fundamental forces: SU (2)L × U (1)Y a unified version of the electromagnetic and weak forces, referred to as the electroweak force, and SU (3) the strong force. The purely electromagnetic interaction (QED) involving only electrically charged particles is represented by the group U (1), while the purely strong interaction (QCD) involving only quarks and gluons is represented by SU (3). Each subgroup has an associated coupling strength and gauge field, as represented in Table 1.1, and the particles can be interpreted as the irreducible representations (multiplets) of these symmetry groups. Theoretical Background 7 Group Coupling constant Gauge field SU(3) gs = √ 4piαS G a µ U(1) e = √ 4piα Aµ SU (2)L g = e/ sin θW sin2θW = g ′2/(g2 + g′2) W aµ U (1)Y g ′ = e/ cos θW Bµ Table 1.1.: Common notation used for the SM coupling constants and associated gauge fields, where αS is the strong coupling, α the electromagnetic coupling, θW the weak mixing angle and e the electromagnetic charge. QED and QCD sectors - Both of these sectors are described by the same lagrangian structure: L = ψ¯(iD −m)ψ − 14(F (a)µν )2 (1.1) where ψ is the fermion (spinor) field, D the covariant derivative and F (a) µν the gauge- invariant field strength tensor, defined in terms of the gauge fields in Table 1.1 as in Equations 1.2-1.3. The first term then represents the kinetic and interaction terms of fermions and the second is the gauge boson kinetic term. However, the different properties of the symmetry groups representing QED and QCD, such as dimensions, commutativity, lead to different physics. In QED, the force is mediated by one massless gauge boson - the photon Aµ, while in QCD there are eight - the gluons Gaµ, where a = 1, .., 8. The non-abelian nature of SU(3) is manifested by the additional term in Equation (1.3), allowing for gluon self-interactions. QED: Fµν = ∂µAν − ∂νAµ (1.2) QCD: F aµν = ∂µG a ν − ∂νGaµ − gsfabcGbµGcν (1.3) The corresponding gauge covariant derivatives are defined as: QED: Dµ = ∂µ + ieQAµ (1.4) QCD: Dµ = ∂µ + igsTaG a µ (1.5) where Q is the generator of U(1) (the electromagnetic charge) and Ta are the SU(3) group generators (the colour charge) of a particular representation (quarks are in the fundamental representation while gluons are in the adjoint representation). QCD is also different from QED in that that the first term of Equation (1.1) requires a 8 Theoretical Background summation over three additional fields, which represents the colours a quark can have, i.e. ψa, a = 1, 2, 3. Electroweak sector - This sector has some significant differences with respect to the QED/QCD sectors. In terms of field content, an isotriplet of gauge fields W iµ (i = 1, 2, 3) couples with strength g to the weak-isospin SU (2)L current, while a single gauge field Bµ couples to the weak-hypercharge U (1)Y current with strength g′/2. T i and Y are the group generators respectively, such that they relate to the U (1) generator as Q = T 3 + Y/2. The SU (2)L current only has left-handed components so it couples to doublets of left-handed fermions, e.g. for the ith lepton family, ψiL = ( νi l−i ) L . SU (2)L is non-abelian so the corresponding field strength W i µν contains additional W iµ self-coupling terms, as with the gluons in QCD. Unlike the purely QED/QCD sectors discussed above, the electroweak sector allows for the Higgs mechanism to yield the masses of the massive SM particles, while still preserving gauge invariance and renormalisation. The masses are revealed by spontaneous symmetry breaking of the electroweak group SU (2)L × U (1)Y when a non-zero vacuum expectation value (vev) of the Higgs field is chosen. Due to this symmetry breaking, the components of the Higgs field are turned into “Goldstone bosons” which are “absorbed” by the other fields in order to acquire mass (or additional degrees of freedom). For the SM, the choice of Higgs field is an isospin SU (2)L doublet of complex scalar fields φ with hypercharge Y = 1, and neutral vev φ0 = √ 1 2 ( 0 v ) . This ensures that the photon remains massless and the electroweak bosons become massive. A key feature is that other choices for the representation of the Higgs field lead to different mass relations to those in Equations 1.6-1.8, which do not necessarily fit the experimental results, e.g. masslessness of the photon, the W/Z ratio, etc. The electroweak sector of the SM is summarised by the Lagrangian in Equation (1.9), where L represents a left-handed fermion doublet, and R a right-handed fermion singlet, and G1 and G2 the arbitrary fermion-Higgs couplings. After the Higgs mechanism, the gauge boson mass terms, Equations 1.6-1.8, follow from the fourth term in Equation (1.9), the fermion masses from the last term, and a neutral Higgs field H(x) with mass mH is the only remnant from the Higgs doublet. Theoretical Background 9 W± = (W 1 ∓ iW 2)/ √ 2 −→ MW = 12vg (1.6) Aµ = cos θWBµ + sin θWW 3 µ −→ MA = 0 (1.7) Zµ = − sin θWBµ + cos θWW 3µ −→ MZ = 12v √ g2 + g′2 (1.8) L =− 1 4 W iµνW µν i − 14BµνBµν  W±, Z, γ kinetic terms and self-interactions (1.9) +L¯γµ ( i∂µ − g 12TiW iµ − g′ Y2Bµ ) L +R¯γµ ( i∂µ − g′ Y2Bµ ) R  lepton and quark kinetic terms and their interactions with W±, Z, γ + ∣∣∣∣(i∂µ − g12TiW iµ − g′Y2 Bµ ) φ ∣∣∣∣2 − V (φ)  W±, Z, γ and Higgs masses and their interactions − (G1L¯φR +G2L¯φcR + h.c.).  lepton and quark masses and their interactions with Higgs Observables - The main theoretical predictions relevant to particle physics experiments are decay rates and cross sections, both of which are derived from the transition probability between an initial and final state. For example, the differential cross- section may be written in symbolic form as: dσ = |M|2 F dLips (1.10) where M is the Lorentz-invariant amplitude or “matrix element” encoding the physics of the process – the type of interaction, particles involved and the mediator 10 Theoretical Background of the interaction (propagators) as found in the SM Lagrangian, As for F , the initial flux, and dLips, the “Lorentz-invariant phase space factor”, they merely serve to impose kinematic constraints on the initial and final states respectively. A key feature of the SM theory is however, that M cannot be solved exactly but rather approximated by the technique of perturbation theory, whereby a series expansion of M is done. The leading-order (LO) term in the series represents the largest contribution to the result, whereas the inclusion of higher-order terms are corrections that make the results more accurate. Renormalisation - As mentioned, the transition amplitude M is calculated with per- turbation theory and the consequence is that the result is only an approximation to the real value. A more accurate result is obtained by including higher-order terms from the perturbation series, which is equivalent to adding more intricate Feynman diagrams as illustrated in Figure 1.1. The problem is that the effect of such corrections can sometimes be significant, e.g. the Lamb shift or charge-screening, and their calculation is also technically challenging. Moreover, the value of the loop four-momentum in the Feynman diagrams is unrestricted, so many of these corrections can result in divergent integrals. The idea of renormalisation therefore came to “rescue” the SM by proving that such divergences cancel out when the observables are redefined in terms of measured values rather than “bare values”. For this, a scale µ characteristic of the experiment must be chosen to relate the observable to its bare value. This is equivalent to having a single Feynman diagram with a running coupling. Equation (1.11) exemplifies the renormalised/running version of the QED coupling resulting in the charge screening effect – as the energy scale Q2 increases, so does the coupling. The evolution of the couplings with the energy scale β(α) = ∂α/∂ ln(µ) is often referred to as the Renormalisation Group Equations (RGEs). QED: α(Q2) = α(µ2) 1− α(µ2) 3pi log Q 2 µ2 (1.11) Theoretical Background 11 Figure 1.1.: Pictorial representation of higher-order corrections to the γ propagator when calculating a cross-section. From [1]. 1.1.2. QCD at Hadron Colliders At the LHC we have proton-proton collisions, i.e. mainly strong interactions which determine the final state. Hence, for this thesis, understanding the role of QCD at hadron colliders was crucial. This section summarises some of these concepts. Figure 1.2.: The parton model description of a hard scattering process. From [3]. Cross section - Although quarks are always found in confined states (hadrons), at high energies (high-momentum transfer Q2) a hadron appears as a sea of quasi-free point-like quarks and gluons (partons) and so, the cross section is dominated by the scattering of quasi-free constituent partons – this is the idea behind the parton model. Consequently, one requires the knowledge of the partons momentum distribution - the parton distribution functions (PDFs). For a hadron-hadron collision, as illustrated in Figure 1.2, if the two incoming hadrons have four-momenta P1 and P2, the 12 Theoretical Background cross-section can be written as: σ(P1, P2) = ∑ i,j ∫ dx1dx2fi(x1, µ 2)fj(x2, µ 2)σˆij(p1, p2, αs(µ 2), Q2/µ2) (1.12) The i and j indices represent the parton types and p1 = x1P1 and p2 = x2P2 the momenta of the partons which participate in the hard-scattering. The PDFs fi(x1, µ 2) represent the probability of finding a parton of type i in the parent hadron, carrying a fraction x1 of its momentum, defined at a factorization scale µ ∼ Q. The short-distance (high Q2) cross section for the process is σˆij and, since in this regime the strong coupling αs is small, σˆij can be calculated using perturbation theory as in QED – as a power series in αS. The break-down of the perturbative approach is at low Q2, where αS is large. Clearly, the effective parton-parton centre- of-mass (c.o.m.) energy √ sˆ is only a fraction √ x1x2 of the total c.o.m. energy√ s and since the PDFs decrease rapidly with x, probing high √ sˆ values implies accumulating correspondingly large integrated luminosities. PDFs - As previously defined, the PDFs are functions of x and Q2 and are directly related to the structure functions Fi(x,Q 2). Being non-perturbative, the structure functions have been extracted from data, an example of which is shown in Figure 1.3(a). In this figure, the parton model prediction of Bjorken scaling (Fi(x,Q 2) → Fi(x) at high Q2) is observed, while the scaling violations become evident at low x, where the gluon density and qq¯ sea effects become significant. As for the proton PDFs, they have been determined from fits to a large set of experimental data, as shown in Figure 1.3(b), where some features are that quarks carry about 50% of the proton’s momentum (gluons carry the rest) and for up and down-type valence quarks uv ∼ 2dv. Similarly, for x < 0.2 gluons dominate. Due to higher-order corrections, the PDFs also have contributions from virtual qq¯ produced by the gluon sea. The uncertainties associated to PDFs can have large effects on cross-section calculations at hadron colliders, e.g. prior to HERA data, the uncertainty on Higgs production at the LHC was ∼ ±25% [7]; which has now been reduced to ∼ ±8% [8]. Running coupling - The running of αs with Q2 follows from the same argument as in QED (see Section 1.1). However, due to the gluon loops from QCD, its behaviour turns out to be opposite to that in QED. Mathematically, the difference lies in the coefficient of log(Q2/µ2) in Equation (1.11), which is positive for QCD. Therefore in this case αs(Q 2) decreases with Q2 as shown in Figure 1.4, so that it is small for short-distance interactions as in the parton model. The phenomenon is known as Theoretical Background 13 Q2 (GeV2) F 2 (x, Q2 ) * 2i x H1 ZEUS BCDMS E665 NMC SLAC 10 -3 10 -2 10 -1 1 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 -1 1 10 10 2 10 3 10 4 10 5 10 6 (a) 0 0.2 0.4 0.6 0.8 1 1.2 10 -4 10 -3 10 -2 10 -1 x x f (x) 0 0.2 0.4 0.6 0.8 1 1.2 10 -4 10 -3 10 -2 10 -1 x x f (x) (b) Figure 1.3.: (a) The proton structure function F p2 measured by different experiments. (b) The proton PDFs as determined in the NNLO MSTW2008 global fit (both figures from [5]). asymptotic freedom and allows the use of a perturbative approach in this regime. For experiments at the LHC, αs ∼ 0.1 and perturbative QCD (pQCD) can be used. A cutoff Q2 ∼ Λ2 is normally used to denote the low-energy scale at which partons hadronise (become strongly bound) and such treatment is no longer valid. Renormalisation and factorisation scales - As previously mentioned (Section 1.1), these scales arise from using a perturbative approach and are defined to play similar roles but at opposite ends of the energy range: through the factorisation scale µF , the bare PDFs absorb the long-distance (“infrared”, i.e. soft and collinear) physics, acquiring a µF dependence, whereas through the renormalisation scale µR the strong coupling absorbs the short-time (“ultraviolet”) physics, acquiring a µR dependence. As discussed, the theoretical prediction at fixed-order will have a dependence on these scales, which becomes less important the more higher-order corrections are included. Confinement and Hadronisation - SU(3) represents the invariance of the strong inter- action under unitary transformations in colour space. A consequence of this group structure is colour confinement - quarks and gluons are confined to bound states of 14 Theoretical Background QCD α (Μ ) = 0.1184 ± 0.0007s Z 0.1 0.2 0.3 0.4 0.5 αs (Q) 1 10 100Q [GeV] Heavy Quarkonia e+e– Annihilation Deep Inelastic Scattering July 2009 Figure 1.4.: The ‘running’ of αs with the energy scale Q, as measured by different processes. From [5]. colourless hadrons, so they are never observed as free particles. The hadron picture becomes relevant in the low-energy regime, for which there is little theoretical understanding as it is non-perturbative (although theoretical advances in this area have become available with time, like lattice QCD). The Lund string model and the cluster model are commonly used to explain hadronisation. The general idea is illustrated in Figure 1.5: after scattering, initially the quarks separate at high velocity, but then a colour flux tube forms between them. The energy stored in the flux tube is sufficient to produce qq¯ pairs and soft radiation (parton showering). This process continues until quarks are bound into colourless hadrons, generally observed as jets in hadron colliders. The non-perturbative part in this process can be factorised out via the fragmentation functions - the final-state analogue of PDFs used for initial-state hadrons. Underlying Event - Due to the composite structure of hadrons, the underlying event (UE) refers to the processes taking place in a hadron collision in addition to the primary hard-scattering - the hadron can be viewed as bunches of incoming partons as depicted in Figure 1.6. The UE includes initial (ISR) and final state radiation (FSR), multiple interactions (scattering between other parton pairs from the same hadron pair), beam remnants (a fragment of the hadron not taking part in the ISR or hard-scattering) and pileup (when more than one hadron in the beam interacts Theoretical Background 15 jet jet space tim e Figure 1.5.: Schematic representation of parton showering and hadronisation in the Lund string model. in a given bunch crossing). Some of these can be modeled with pQCD. Depending on the analysis, UE contributions can sometimes be significant [9]. Figure 1.6.: Pictorial representation of the underlying event in a hadron-hadron collision. Each hadron can be pictured as a ‘beam’ of partons, which is why other interactions occurs apart from the hard-scattering like ISR/FSR. In addition, other hadrons from the beam can collide in the same bunch-crossing causing ‘pileup’. 16 Theoretical Background 1.1.3. Problems of the Standard Model The scientific community’s confidence in the SM theory today is the result of the progressive confirmation by experiment of many of its predictions. Some of these tests have been precise enough to validate even radiative corrections - the value of the QED coupling has been tested to 0.37 ppb from the e± magnetic moment[10], the Z boson mass to 23 ppm from e+e− → hadrons [11] and Fermi’s constant to 8.6 ppm from the muon lifetime [12]. Similarly the agreement of numerous QCD and electroweak predictions with data has been remarkable, as exemplified for hadron collider physics in Figure 1.7. However, there are still many aspects of the model which are poorly understood, most likely indicating the presence of new physics. Recalling Fermi’s theory of beta decay (1933) which treated the interaction as pointlike and yet had great phenomenological success, the SM can similarly be regarded as an effective field theory at the energies probed so far. This section lists some of the aspects for which the model has little or no coverage at all. Free parameters - The predictive power of the SM appears to depend on the input of 19 fundamental parameters, listed in Table 1.2, and whose values need to be well- measured. Some of them have large theory uncertainties (e.g. no radiative corrections available) or are experimentally limited by precision or at most constrained from data. Moreover, many depend on the input values of other free parameters, leading to differences and correlations in global fits. To avoid such problems, it would be desirable to have a model involving fewer fundamental parameters, from which the others could be derived. The SM free parameters 3 gauge couplings gs, g, g ′ 9 fermion masses 3 fermion CKM mixing angles 1 CKM phase 2 Higgs vev and quartic coupling v, λ 1 QCD CP -violating parameter θ Table 1.2.: The SM 19 fundamental parameters whose values are chosen to fit the data. Measurements exist for the couplings, fermion masses and Vij [5], but only limits for v, λ and θ. The latter is constrained by measurements of the neutron electric dipole moment [14]. Theoretical Background 17 1 10 10 2 10 3 10 10 2 10 3 inclusive jet production in hadron-induced processes fastNLO hepforge.cedar.ac.uk/fastnlo pp DIS pp-bar √s = 200 GeV √s = 300 GeV √s = 318 GeV √s = 546 GeV √s = 630 GeV √s = 1800 GeV √s = 1960 GeV STAR 0.2 < |y| < 0.8 H1 150 < Q2 < 200 GeV2 H1 200 < Q2 < 300 GeV2 H1 300 < Q2 < 600 GeV2 H1 600 < Q2 < 3000 GeV2 ZEUS 125 < Q2 < 250 GeV2 ZEUS 250 < Q2 < 500 GeV2 ZEUS 500 < Q2 < 1000 GeV2 ZEUS 1000 < Q2 < 2000 GeV2 ZEUS 2000 < Q2 < 5000 GeV2 CDF 0.1 < |y| < 0.7 DØ |y| < 0.5 CDF 0.1 < |y| < 0.7 DØ 0.0 < |y| < 0.5 DØ 0.5 < |y| < 1.0 CDF cone algorithm CDF kT algorithm (× 400) (× 100) (× 35) (× 16) (× 6) (× 3) (× 1) all pQCD calculations using NLOJET++ with fastNLO: αs(MZ)=0.118 | CTEQ6.1M PDFs | µr = µf = pT jet NLO plus non-perturbative corrections | pp, pp: incl. threshold corrections (2-loop) pT (GeV/c) da ta / th eo ry (a) W Z tt t WW WZ ZZ [pb ] to ta l σ 10 210 310 410 510 -14.7 fb -11.0 fb -14.7 fb -10.7 fb -11.0 fb -135 pb -135 pb Data 2010 Data 2011 Theory ATLAS Preliminary -1 L dt = 0.035 - 4.7 fb∫ = 7 TeVs - (b) Figure 1.7.: (a) A compilation of QCD data-over-theory ratios for inclusive jet cross sections measured in different hadron-induced processes at different center-of-mass energies (from [5]). (b) Summary of several Standard Model measurements in ATLAS compared to the theoretical expectations (from [13]). All theoretical expectations are calculated at NLO or higher. 18 Theoretical Background Neutrino oscillations - There is now convincing experimental evidence for neutrino masses (m ∼<2 eV [5]) and yet neutrinos are assumed massless in the SM. Moreover, with 3 light Majorana neutrinos, there would be 9 additional free parameters from their masses, mixing angles and phases. Precision tests deviations - Some measurements show relatively large discrepancies from the SM prediction, like the measurement of the anomalous magnetic moment of the muon by 2.5σ [5]. Exclusion of gravity - Being a fundamental interaction, it seems unnatural that it is excluded from a framework which describes the other interactions. Choice of gauge group - The choice SU (3) × SU (2)L × U (1)Y is rather arbitrary and perhaps a different group structure could explain better the new physics or the poorly understood sectors. A famous example is the Georgi-Glashow model (1974) [15] with SU (5) ⊃ SU (3)× SU (2)× U (1) allowing for lepton/baryon number violation like proton decay. Although the latter has tight limits set by experiments [16], the model sheds light on gauge coupling unification, as well as charge quantisation. Origin of mass - The model assumes this is due to the Higgs mechanism but as of the time of writing, only limits have been set on the existence of the Higgs boson. Some recent ATLAS studies exclude at 95% CL the mass ranges 112.9-115.5 GeV, 131-238 GeV and 251-466 GeV, while the range 124-519 GeV is expected to be excluded in the absence of signal [17]. Matter-Antimatter asymmetry - The amount of CP-violation in the SM cannot account for the large imbalance observed in the universe, e.g. the baryon-to-photon ratio is too big (η ∼ 10−10 [5]). Similarly, the latest constraints on the QCD “θ parameter” (|θ| < 10−10 [5, 14]) yield no significant CP -violation in QCD (“strong CP problem”). Naturalness/Hierarchy problem - Even assuming the existence of the Higgs boson, unless there is an “unnatural” fine-tuning cancellation of its radiative corrections, the Higgs mass value diverges (more details in Section 1.2.1). Dark matter and dark energy - Plenty of cosmological evidence, like recent CMB results, yield a small baryon density in the universe (Ωb = 0.0227 ± 0.0006 [18]) but still much larger than the density of luminous matter. This indicates most baryons are optically dark. Moreover, the total matter density (Ωm = 0.133± 0.006) suggests that most matter in the universe (∼ 83%) takes a cold, weakly-interacting, non- baryonic form, referred to as cold dark matter Ωcdm, so that Ωm = Ωcdm + Ωb. In Theoretical Background 19 addition, dark energy is needed to explain both the flatness of the universe and the observed accelerated expansion. Overall, with respect to the total mass-energy density, dark-matter constitutes ∼ 23% and dark-energy ∼ 72% [18]. These huge proportions of the universe are clearly not covered by the SM. 1.2. Overview of Supersymmetry This section aims to provide a summary of Supersymmetry (SUSY) to cover some basic concepts and ideas relevant to the work presented in this thesis, and particularly relevant to Section 5.6. The summary is given in three parts: Section 1.2.1 presents the motivation for the theory; Section 1.2.2 introduces the MSSM, being the simplest and most widely- studied SUSY model; and Section 1.2.3 discusses the phenomenology expected at hadron colliders, in particular at the LHC, as well as the most popular types of SUSY searches performed in ATLAS. The content and notation used in Sections 1.2.1-1.2.2 are mainly based on references [5, 6, 19]. 1.2.1. Motivation The current problems of the SM discussed in Section 1.1.3 made clear that there is a need of an extension or theory which can solve at least one of these problems - this is the motivation behind BSM theories like Supersymmetry (SUSY). SUSY is a very popular BSM theory because: (i) it can potentially solve more than one of these problems, (ii) the first signs of it are expected at the energies of current particle colliders, and (iii) its beautiful mathematical structure respects the fundamental principles of the SM, like gauge invariance and symmetry. Although other BSM theories exist, few of them are as appealing as SUSY. Initiated around the 1970’s, SUSY was postulated as the only possible extension of the spacetime symmetries in the SM by transforming fermions into bosons and vice versa [20,21]. However, if this symmetry was exact, each SM particle would have a superpartner with the same quantum numbers and mass, only differing by half a unit of spin. Because no such particles have been observed so far, if it exists, SUSY must be a broken symmetry. SUSY has the nice property of offering solutions to the following major SM problems, if it shows up at the TeV scale: 20 Theoretical Background Naturalness/Hierarchy problem - As discussed in Section 1.1.3, the large hierarchy of energy scales between the electroweak and Planck scale seems unnatural. Rather, new physics is expected to appear just after the electroweak scale where the SM becomes ill-defined, e.g. when the Higgs mass gets unacceptably large loop corrections. With SUSY representing the new physics, the UV corrections are cancelled by the superpartners equivalents, as illustrated in Figure 1.8(a). For the remaining corrections to be acceptable, the superpartners masses must be around the TeV scale. Gauge coupling unification - The evolution of the three SM couplings is determined by the particle content . Currently these couplings do not meet at a common energy scale, but this would be theoretically appealing as it could involve a single unified gauge group rather than the current SM product group. With the addition of SUSY at the electroweak scale, convergence of the couplings (potentially including that of gravity) is projected at some high-energy scale, e.g. 1016 GeV [6], Figure 1.8(b). Dark matter - This problem was already discussed in Section 1.1.3. With SUSY, many models, e.g. with R-parity conserved (Section 1.2.2) predict the existence of a stable weakly interacting massive particle (WIMP), which could make up for the observed dark matter or at least some of it. (a) (b) Figure 1.8.: (a) Cancellation of the largest corrections to the Higgs boson mass from the top quark loop via its scalar superpartner loop. The remaining contributions are logarithmic. (b) Expected unification of gauge couplings at high-energies with SUSY, from [1]. Theoretical Background 21 1.2.2. The MSSM The Minimal Supersymmetric extension of the SM (MSSM) consists of the addition of one SUSY partner for every SM particle and an enlarged Higgs sector. The superpartners fields are paired with the SM fields via superfields, as shown in Table 1.3. Two Higgs doublets, with vev’s vu and vd, are required (to cancel gauge anomalies introduced by the higgsinos and to give masses to the up-type and down-type quarks separately). The unbroken MSSM Lagrangian is like the SM Lagrangian but with the addition of a superpotential – a function of superfields, where the µ parameter is introduced as the mass parameter of the Higgs sector. As in the SM, all the terms in the MSSM Lagrangian must be renormalisable and satisfy the SM SU (3)× SU (2)L × U (1)Y gauge invariance, as well as the experimentally-observed B-L conservation (B =baryon number, L =lepton number). For the SUSY-breaking part, all allowed soft terms, i.e. those which do not introduce quadratic divergences, are added by hand (see below). To generate nonzero neutrino masses, additional structure is needed, as discussed in [5]. Field Content of the MSSM Superfields Bosons Fermions SU(3) SU (2)L U (1)Y Gauge gluon/gluino Gˆ g g˜ 8 1 0 gauge/gaugino Vˆ W±, W 0 W˜±, W˜ 0 1 3 0 Vˆ ′ B B˜ 1 1 0 Matter slepton/lepton Lˆ L˜ = (ν˜, e˜−)L (ν, e−)L 1 2 -1 Eˆc E˜ = e˜+R e˜ c L 1 1 -2 squark/quark Qˆ Q˜ = (u˜L, d˜L) (u, d)L 3 2 1/3 Uˆ c U˜ c = u˜∗R u c L 3 1 4/3 Dˆc D˜c = d˜∗R d c L 3 1 -2/3 higgs/higgsino Hˆd H i d (H˜ 0 d , H˜ − d )L 1 2 -1 Hˆu H i u (H˜ + u , H˜ 0 u)L 1 2 1 Table 1.3.: The field content of the MSSM and their SU (3) × SU (2)L × U (1)Y quantum numbers (only one generation of quarks and leptons is shown). The superfield notation is also shown. For each lepton, quark and Higgs super-multiplet, there is a corresponding antiparticle multiplet of charge-conjugated fermions and their associated scalar partners (also not shown). R-parity and LSP: A consequence of imposing B-L conservation in the MSSM is R-parity conservation (RPC). Since R-parity is defined as R = (−1)3(B−L)+2S for a 22 Theoretical Background particle of spin S, R-parity differentiates SM from SUSY particles (the first have R = 1 whereas the second have R = −1). Hence, with RPC, sparticles could be produced from SM interactions in pairs, e.g. pp→ g˜g˜. The sparticles would then decay (possibly via a cascade) into a SM particle plus another lighter sparticle, e.g. g˜ → q¯q˜. Being stable, the lightest SUSY particle (LSP) would be produced at the end of the decay chain, e.g. q˜ → qχ˜01. Given cosmological and experimental constraints (see Section 1.1.3), the LSP must also be weakly-interacting. Symmetry breaking: This is one of the least understood sectors of the theory and hence the one generating the largest number of extra parameters (∼ 100 [5]). Unlike the Higgs mechanism in the SM, in SUSY the breaking terms Lsoft are explicitly added to the Lagrangian. They consist of the following: (i) trilinear scalar interactions 1 3! A˜ijkφiφjφk + h.c.; (ii) bilinear scalar interactions 1 2 b˜ijφiφj + h.c.; (iii) scalar mass-squares m 2 ijφ † iφj and (iv) gaugino masses 1 2 Maλ aλa + h.c. They are referred to as “soft” terms because the breaking scale is related to the electroweak symmetry breaking scale in order to guarantee a solution to the hierarchy problem. Two sectors are defined: the visible (MSSM particles) and the hidden (new particles decoupled from the visible sector). Messenger particles mediate these two sectors and transmit to the visible sector the SUSY-breaking originated in the hidden sector. The most popular models of soft SUSY-breaking are: • Gravity-mediated: these are the most widely-studied models. The messenger is Planck scale physics but there is no role for the gravitino G˜ in the phenomenology un- less it is the LSP. A constrained-model example is mSUGRA (see “Phenomenological Models” below). • Gauge-mediated: the messengers have SU (3)×SU (2)L×U (1)Y quantum numbers and SUSY breaking is transmitted via the SM gauge interactions; often G˜ is the LSP. A constrained-model example is GMSB (see “Phenomenological Models” below). Other mechanism also explored, although less than the previous two, is: • Extra Dimensions: visible and hidden sectors are on two separate branes and messengers live on the “bulk”. Physical states: Analogous to the SM, after electroweak (EW) symmetry is broken, the MSSM fields mix to form the physical mass states listed in Table 1.4. In practice (due to phenomenological constraints from FCNCs), the mixing of the lighter two sfermion generations is neglected and taken to be “mass-degenerate”. In contrast, due to the large mass of the SM third-generation, a significant L-R mixing can take place for third Theoretical Background 23 generation squarks, allowing them to be distinguishable from the other generations and much lighter – analogous to the seesaw mechanism in neutrinos. A typical SUSY mass spectrum is illustrated in Figure 1.9. As for the Higgs sector, using two Higgs doublets results in 5 physical (spin-0) Higgs bosons: two charged H˜±, two neutral CP-even h0 and H0 (mh < mH), and one neutral CP-odd A 0. Their masses depend only on tan β = vu/vd and one of the Higgs masses (typically mA). B˜0, W˜ 0, H˜0u, H˜ 0 d → neutralinos: χ˜01, χ˜02, χ˜03, χ˜04 W˜±, H˜+u , H˜ − d → charginos: χ˜±1 , χ˜±2 τ˜L, τ˜R → stau: τ˜1, τ˜2 (t˜L, t˜R), (b˜L, b˜R) → stop, sbottom: (t˜1, t˜2), (b˜1, b˜2) Table 1.4.: Mixing in the MSSM. Line combinations of neutral gauginos and higgsinos form neutralinos, whereas the charginos result from charged gauginos and higgsinos. Phenomenological Models The MSSM introduces 124 parameters of which only 18 are purely SM [5]. Fortunately, it is possible to make useful predictions at low-energies (electroweak scale) by constraining this parameter space from the direct and indirect experimental results to date, as well as other simplifying assumptions. Indirect constraints come from the relic dark-matter density and precision electroweak data. These restrict the nature of the LSP and suppress lepton number violation, FCNCs and additional sources of CP-violation. Direct constraints have been obtained from direct SUSY searches, e.g. at LEP, the Tevatron and LHC. As for the additional simplifying assumptions, the following are typically the approaches taken: Constrained Models: In these, a particular SUSY-breaking mechanism and unification at the GUT scale are assumed, e.g. the top-down approach assumes a unified gaugino mass at high-energies so that the low-energy masses are related, e.g. M3 ∼ 3.5M2, M1 ∼ 0.5M2 [5]. Within these type of models, the most popular are: • mSUGRA: the scalars, gauginos and A-term masses (m0, m1/2, A0 respectively) unify at the GUT scale. With this, the number of parameters dramatically reduces to 5 (plus the 18 from the SM): m0, A0, m1/2, tan β, sign(µ) 24 Theoretical Background The RGEs are then used to predict values of the parameters at the electroweak scale, e.g. first two squark generations are roughly degenerate while the third is lighter; sleptons are lighter than squarks and the LSP is the lightest neutralino χ˜01, as shown in Figure 1.9. Although perhaps too simplistic, this model is one of the most widely used at present colliders to set exclusion limits on SUSY (e.g. see Section 5.6.3). • GMSB: an effective mass scale Λ ∼ 100 TeV determines the low-energy scalar and gaugino masses through loop effects. A light gravitino is the LSP but the NLSP is really what determines the phenomenology, e.g. typically the NLSP is lightest neutralino or stau, which then decays into its superpartner plus gravitino χ˜01 → γ/Z + G˜ or τ˜±R → τ±G˜. Different choices of NLSP lead to a variety of final states, e.g. a long-lived χ˜ 0 1 decaying outside detector leads to EmissT + leptons + jets, whereas χ˜ 0 1 → γG˜ occurring inside detector leads to final states of EmissT +γ. The number of SUSY parameters in this model is six: Fm, Mm, N5, Cgrav, tan β, sign(µ) where Fm is the SUSY-breaking scale, Mm the messenger scale, N5 the number of messenger fields and Cgrav the couplings for decays into G˜. • AMSB: this is a special type of extra-dimensions gravity-mediated model where the SUSY-breaking is communicated through the conformal anomaly [22]. Typically the LSP is a wino W˜ 0 and charginos behave like a stable massive particles. Simplified (“Toy”) Models: These models take a different approach to constrained models by focusing on a subsector of the SUSY spectrum. In this case, the simplifying assumptions are on the masses, hierarchies and decay-chains of particles. RPV: Models with R-parity violation (RPV) exist but since they allow an unacceptably fast proton decay[16] and do not provide a dark matter candidate, RPC models have been more favoured. R-parity violating scenarios also have the disadvantage of introducing more parameters than in RPC scenarios since B-L violation is allowed. Yet, they successfully incorporate neutrino masses and escape many bounds set by the RPC-based searches, which is why these models are still studied. The RPV terms in the Lagrangian allow the LSP and other sparticles to decay to SM ones. However, phenomenological constraints derived from data have been used to set severe limits on the couplings of these terms. Theoretical Background 25 0 100 200 300 400 500 600 700 m [GeV] mSUGRA SPS 1a′/SPA l˜R l˜L ν˜l τ˜1 τ˜2 ν˜τ χ˜01 χ˜02 χ˜03 χ˜04 χ˜±1 χ˜±2 q˜R q˜L g˜ t˜1 t˜2 b˜1 b˜2 h0 H0, A0 H ± Figure 1.9.: Mass spectrum of a reference point in mSUGRA, (SPS 1a’). The masses of the first two generations are denoted collectively as q˜, ˜`and ν˜l from [1]. Problems of the MSSM Paradoxically, although this is the most accepted model in SUSY, the MSSM has its own problems: the ‘µ-problem’, similar to the SM hierarchy problem already discussed, requires µ to be of the order of the electroweak scale, which is known to be much smaller than the Planck scale. Moreover, as will be discussed in Chapter 6, the present experimental limits on SUSY are now strong enough to re-evaluate whether SUSY can still address the fine-tuning issue with respect to the Higgs mass or the relic density from cold dark matter. This part will be discussed further in the closing chapter. 26 Theoretical Background 1.2.3. Searches at the LHC Phenomenology Because of the higher c.o.m. energy, the SUSY mass reach at the LHC will largely exceed that from LEP and the Tevatron. In pp collisions, coloured sparticles, namely squarks and gluinos, are expected to be the most copiously produced, as suggested by Figure 1.10. The diverse MSSM phenomenology which motivates the different SUSY searches at the LHC is exemplified in Figure 1.11. RPC scenarios are characterised by sparticle pair- production (with the dominant hard-process depending on the mass-hierarchy assumed, as shown in Table 1.5) and missing energy from the LSP which is stable and weakly- interacting. In addition, with RPC, the breaking mechanism determines the nature of the LSP/NLSP, which in turn determines the final state. In the RPV scenario, the final state is determined by whether the sparticles are long- or short-lived. Unlike in e+e− colliders, in hadron colliders the c.o.m. energy of the colliding partons √ sˆ is not known but rather its probability density as determined from PDFs (see Section 1.1.2). Since most of the beam remnants escape undetected in the beam pipe, only conservation of momentum in the plane transverse to the beam direction can be used to infer this imbalance – hence the definition of missing transverse energy EmissT . The key point is that the RPC final-state signature is EmissT +X, where X depends on more specific model details like the breaking mechanism and the nature of LSP/NLSP. 10 -3 10 -2 10 -1 1 10 100 200 300 400 500 600 700 800 900 χ˜2oχ˜1+ ν˜eν˜e* t˜1t˜1* q˜q˜ q˜q˜* g˜g˜ q˜g˜ χ˜2og˜ χ˜2oq˜LO m average [GeV] σtot[pb]: pp → SUSY √S = 7 TeV Prospino2.1 Figure 1.10.: Total cross-section (in picobarns) for sparticle production as a function of mass, representative of the LHC. Clearly the cross-section is highest for light squarks and gluinos. From [23]. Theoretical Background 27 RPC   RPV   •  LSP  decays   SUGRA/   AMSB   GMSB   LSP  =    χ0 1   •  pair  produced:     •  invisible  &  stable  LSP:   •  decay  chains       q q, q g, g g ETmiss LSP  =     G coloured  spar9cles    q, g long-­‐lived   resonances   X = l + jets ETmiss + X X = γγ inside   detector   outside   detector   displaced   vertex   ETmissdisappearing  track   vτ → eµ g→ jets NLSP  =    χ0 1 Figure 1.11.: Schematic chart illustrating the diverse SUSY (MSSM) phenomenology expected at the LHC which motivates the search for different final-state signatures. Mass Dominant canonical SUSY hierarchy process Typical Final-state decays signature mq˜  mg˜ pp→ q˜ ¯˜q q˜ → qχ˜01 EmissT + 2j mq˜ ≈ mg˜ pp→ q˜g˜ q˜ → q χ˜01 EmissT + 3j g˜ → q¯q˜/q ¯˜q → q¯qχ˜01 mq˜  mg˜ pp→ g˜g˜ g˜ → q¯q˜/q ¯˜q → q¯qχ˜01 EmissT + 4j Table 1.5.: Squark and gluino pair-production is expected to dominate SUSY processes at the LHC (see Figure 1.10) and the dominant hard-process depends on the mass-hierarchy assumed. In the canonical scenario, their typical decays lead to signatures of EmissT from neutralinos and a number of high-pT jets from the daughter quarks after hadronisation, although soft jets from ISR and FSR may increase the jet multiplicities. In the popular “canonical scenario” (RPC, mSUGRA-breaking with χ˜ 0 1 as LSP), assumed in Table 1.5, the following applies: • Neutralinos: Being non-coloured, their direct production at the LHC is suppressed. There are four of them, all electrically-neutral. They are Majorana (their own antiparticles) and appear in the cascade decays of heavier sparticles. As mentioned, the lightest is the LSP (the source of EmissT ), produced at the end of the decay-chain. 28 Theoretical Background The heavier neutralinos typically decay to lighter neutralinos via on-shell Z or charginos via on-shell W±. The subsequent decay of Z and W± can result in final-states involving leptons and neutrinos. • Charginos: There are two types, each of which can be positively- or negatively- charged. The heavier one can decay to the lighter one via an on-shell Z. Both can decay to neutralinos via an on-shell W±. Again, the subsequent decay of Z and W± can result in final-states involving leptons and neutrinos, as shown in Table 1.6. • Squarks: They decay to their SM partners (quarks) plus charginos or neutralinos. Each daughter quark undergoes hadronisation and is seen in its final-state as a high-pT jet, as shown in Table 1.5, although additional (softer) jets from ISR and FSR may increase the jet multiplicities (see Section 1.1.2). • Gluinos: Having only colour-charge, they can only decay to quarks plus squarks. Since they are also Majorana, they decay to q¯q˜ or q ¯˜q with equal probability. Their final-states hence relate to those from squarks described above. • Sleptons: If light enough, they are more likely to be produced in the decays of charginos (→ ˜`±ν) and neutralinos (→ ˜`+ ˜`−). Search Strategy As this thesis is based on data from the ATLAS experiment at the LHC, the rest of this section is specific to ATLAS, although for CMS –the other multi-purpose experiment at the LHC– the results and strategies are very similar. This section also focuses on the RPC-based searches (often referred to here also as “EmissT +X”), as these are the types of searches in which this thesis specialises. The strategy described however, also applies to other BSM searches. Theoretical Background 29 SUSY   Target  1   Target  2   Target  3   SR1   SR2   SR3   SR1   SR2   SR1   BG1   BG2   BG3   BG1   BG2   BG3   BG1   BG2   BG3   BG1   BG2   BG1   BG2   BG1   BG2   BG3   BG4   Limits   Model  1   Model  2   Model  3   Limits   Model  1   Model  2   Limits   Model  1   Figure 1.12.: Schematic chart illustrating the general search strategy used when looking for BSM signals like SUSY. First, the search is split into different final-state targets. For each of the targets, a number of Signal Regions (SRs) are defined, and for each of these, the different SM backgrounds (BGs) are estimated. If no excess is found above the SM expectation in the SR, the information from all SRs is combined to set the best limits on different SUSY models. The typical experimental strategy for a BSM search like SUSY is illustrated in Figure 1.12, where the following steps are illustrated: i. Target search: Given the different possible final-state signatures, in ATLAS the SUSY searches are split according to final-state signature and the trade-off between model-sensitivity and model-independence. Table 1.6 shows the main EmissT + X searches currently targeted in ATLAS. The first four target general squark-gluino pair-production but cover different final-states. The searches for b-jets final-states target specifically the production of third generation squarks, which given its sizable mass-state mixing, could be the lightest and most accessible at the LHC. The dilepton and diphoton searches are meant to be sensitive to direct gaugino pair- production, e.g. if squarks and gluinos are heavier than the lightest neutralino and chargino. ii. Signal Region definition: For each search target, one or more Signal Regions (SRs) are defined, which are simply event selections that maximise sensitivity to BSM models while maintaining enough statistics for a meaningful signal. The 30 Theoretical Background RPC (EmissT +X) SUSY- Search Targets X 0` +jets multijets 1`+ jets 2`+ jets 0`+ b-jets 1`+ b-jets γγ pp→ q˜q˜/q˜g˜/g˜g˜ pp→ b˜b˜/g˜g˜ pp→ t˜t˜/g˜g˜ pp→ χ˜0i χ˜±j , q˜ → qχ˜01 q˜ → qχ˜01 q˜ → qχ˜± pp→ χ˜0i χ˜±j /χ˜02χ˜02 g˜ → b˜b g˜ → t˜t χ˜02χ˜02 g˜ → q¯q˜/q ¯˜q g˜ → q¯q˜/q ¯˜q g˜ → qq¯′χ˜± χ˜±i → l±νχ˜0j b˜→ bχ˜01 t˜→ bχ˜±1 χ˜01 → γG˜ short long χ˜±i → l±νχ˜0j χ˜±1 → χ˜01l±ν cascades cascades χ˜0i → l±l∓χ˜0j χ˜±i → l±l∓χ˜±j Table 1.6.: Main decay channels and final-state signatures targeted in RPC searches in ATLAS. In the “multijets” search, the target is final-states with ≥ 6-8 jets. RPC (EmissT +X) SUSY- Signal Regions Requirement 0` +jets multijets 1`+ jets 2`+ jets 0`+ b-jets 1`+ b-jets γγ # jets, pT(ji) 4 4 4 4 4 4 - EmissT 4 - 4 4 4 4 4 ∆φ(ji, E miss T ) 4 - 4 - 4 4 -EmissT /meff meff other ∆Rjj mT mll # b-jets mT pT(γ) EmissT / √ HT SS,OS # b-jets E iso T (γ) discriminating meff E miss T / √ HT meff E miss T meff ,mCT meff E miss T variable Table 1.7.: Similarities and differences in the definition of the SRs for the different RPC searches. Requirements on EmissT and jets are common, while others are specific to the search target. ∆Rjj is the jet-jet separation, HT = ∑ pT(ji), “SS,OS” is same/opposite-signs, mCT the co-transverse mass and the other variables are defined elsewhere in the text. Theoretical Background 31 new physics is therefore searched in the SRs as an excess of events over the SM background expectation. Usually more than one SR is defined to be sensitive to different models. Table 1.7 summarises the main characteristics defining the SRs for the RPC searches, from which is clear that requirements on EmissT and jets are common. iii. Background Estimation Even in the SRs, the great difference in cross-sections between BSM and most SM processes (e.g. for SUSY ∼ 1 pb versus ∼ 80 mb) makes the distinction of new signals very challenging. Therefore, resolving non- SM excesses is only possible when all the corresponding backgrounds have been identified and estimated. The backgrounds contribute differently depending on the search target, as shown in Table 1.8, but also depending on the SR, hence why each background has to be estimated for each SR, as illustrated in Figure 1.12. Different background-estimation techniques are used, though those derived from real data, known as data-driven, are much more preferred over Monte Carlo simulation. Data-driven estimates make use of Control Regions (CRs), samples associated to a particular background process, from which predictions in the SR can be obtained. In the case of SUSY RPC searches, the main backgrounds come from true EmissT sources, e.g. W (→ `ν) + jets, as well as from fake EmissT sources, e.g. jet-energy mismeasurements (often referred as the ‘QCD background’). As this thesis specialises in an estimation method for the Z + jets background, this topic will be covered in full detail over the following chapters. RPC (EmissT +X) SUSY- Main SM Backgrounds 0` +jets multijets 1`+ jets 2`+ jets 0`+ b-jets 1`+ b-jets γγ W/Z QCD tt¯ tt¯+ t tt¯ tt¯ QCD t¯t + t tt¯ W/Z Z W/Z W/Z W QCD W/Z diboson diboson diboson diboson tt¯ QCD fake lep QCD QCD Z Table 1.8.: Dominant SM contributions to the RPC SUSY searches in ATLAS (tt¯+ t means tt¯ plus single top production). Searches requiring large EmissT in their SRs suffer more from real-EmissT backgrounds, while those requiring large jet multiplicities suffer more from QCD backgrounds. When only tt¯ is shown, it means the single top contribution is negligible. 32 Theoretical Background iv. Excess search: As mentioned, the data is then compared to the SM background expectation in each of the SRs to search for non-SM excesses, after considering all the associated experimental uncertainties, e.g. jet-energy scale and resolution, trigger, efficiencies, etc; as well as theoretical uncertainties, e.g. PDFs, renormalisation scale, etc. v. Limit setting: Finally, if no excess is found, model-independent limits (on the so-called “effective SUSY cross-section” σSUSY × A× ε where A is acceptance and ε is efficiency) are set by combining the information of all SRs, using different statistical methods. In ATLAS, the statistical method is usually the CLs method at 95% confidence level [24]. The results are then interpreted with respect to either simplified and constrained models, examples of which were discussed in Section 1.2.2. Usually, if there is more than one SR, the one with best expected limit is chosen to maximise the reach. Chapter 2. ATLAS and the LHC Having covered the necessary theoretical background in the previous chapter, the aim now is to summarise the experimental setup used for the experimental studies presented in Chapter 5. First, Section 2.1 gives an overview of the LHC machine as this is the particle collider which produces the collision events of the data used. For this part, the main references used were [25–27]. Section 2.2 then follows with a brief description of ATLAS – the particle detector used to record and measure the LHC collision events. For this, the main references used were [28,29]. 2.1. The LHC The Large Hadron Collider (LHC) is at present the world’s highest energy particle accelerator. It currently collides head-on beams of protons and, for a short time at the end of the year, lead ions. The LHC aims to be sensitive to new physics, but the rate of events of a given type Nevent is fixed by the cross section of the relevant scattering process σevent and the luminosity L : Nevent = L σevent (2.1) Indeed, the rarer the event, the smaller σevent is, and so, achieving the highest luminosity is a top priority for the LHC, since unlike σevent which is fixed, L can be optimised from beam parameters according to the equation: L ∼ frN 2 b nb 4piσ2 F (2.2) 33 34 ATLAS and the LHC where fr is the machine revolution frequency (set by the synchrotron radius and the speed of light c), Nb the number of protons per bunch, nb the number of bunches per beam, σ the transverse beam size at the interaction point (IP), and F the reduction factor due to the crossing angle at the IP (if the collisions1 are not exactly head-on). The beam size σ is frequently expressed in terms of its beta (amplitude) function at the IP (β?), the normalised transverse emittance εN (an energy-invariant measure of the phase space occupied by the particles of the beam as it travels, reflecting the quality of the initial bunch preparation) and the relativistic gamma factor γr = E/m as σ2 = β?εN/γr. Therefore, to optimise the luminosity, the beam should have the largest number of bunches, with the highest population, colliding at locations where the beam optics provides the lowest possible β?. At the LHC, the lowest β? happens at four IP’s, as shown in Figure 2.1(a), each of which houses a particle detector: ATLAS and CMS are the largest and multi-purpose detectors, aimed for the LHC’s design peak luminosity (1034 cm−2s−1); LHCb is smaller and dedicated to B-physics, so in order to have cleaner signatures (less pileup, see Section 2.2.4), it aims at a lower peak luminosity (1032 cm−2s−1) by locally defocussing the beams at its IP (higher β?). ALICE is dedicated to the heavy-ion runs, so it only operates at the peak luminosity during this time. To understand better why the LHC is the most powerful collider nowadays, Table 2.1 compares its design beam parameters to those of the Tevatron, which used to be the most powerful. 2.1.1. Operation Cycle An ideal LHC beam cycle is shown in Figure 2.1(b). For the “proton run”, before being injected into the LHC, protons are subject to various stages of acceleration and beam preparation. First, they are accelerated from the proton source to energies of ∼ 50 MeV at the CERN Linear Accelerator (LINAC2). Then, they are transferred to successive proton synchrotrons for further acceleration, bunch structure definition and setting the filling scheme: from the Proton Synchroton Booster (PSB, 1.4 GeV) to the Proton Synchroton (PS, 25 GeV) and then to the Super Proton Synchroton (SPS, 450 GeV). After this, they are injected into the LHC in the form of two oppositely-circulating beams, each of which is in a separate pipe throughout most of the ring, except around the IP’s where the same pipe is shared. Placed along the ring, superconducting (2 K, liquid He) dipole magnets ensure the beam’s fixed orbit, while quadrupoles provide 1Throughout the text, the term “collision” will be used to refer to one proton-proton interaction. ATLAS and the LHC 35 the transverse focusing and RF cavities the accelerating voltage. Throughout the pipe, ultra-high vacuum systems minimise proton collisions with gas molecules and particles produced by synchrotron radiation. The magnetic field in the dipole magnets is then increased to 8.3 T (ramping) as the protons are accelerated to the maximum collision energy, which in 2010 and 2011 was 7 TeV (3.5 TeV per beam). At this energy, the beams are squeezed as much as possible to achieve a low β?, after which stable beams for physics may be declared. This is the period during which the experiments record data for physics analyses. The data-taking period usually lasts as long as the beam’s luminosity lifetime (∼ 15 hours [30]). Tevatron (Fermilab) LHC (CERN) Design Oct-2011 Physics start date 1987 2009 - Particles collided p¯p pp - Circumference (km) 6 27 - Beam energy (TeV) 0.98 7.0 3.5 Peak luminosity (1033cm−2s−1) 0.402 10 3.5 Bunch spacing (ns) 396 25 25 Nb (10 12) p:2.6, p¯:0. 9 0.115 0.140 nb 36 2808 1380 fr (Hz) 47700 11245 - β? (m) 0.35 0.55 1 γr 1045 7461 - εN (µm rad) - 3.75 - σ (µm) 66 16 - F 1 0.85 - Magnetic field (T) 4.4 8.3 - Table 2.1.: Nominal Tevatron parameters [31, 32] compared to those from the LHC design [26, 33] and values observed for fill 2219 on Oct-2011 [27]. The symbols are defined elsewhere in the text. 2.1.2. Performance A historical overview of the LHC since it started operation is shown in Table 2.2. The progress in machine development has clearly led to the optimisation of the beam parameters and more uninterrupted operations. Figure 2.2 shows the integrated luminosity 36 ATLAS and the LHC (a) (b) Figure 2.1.: (a) Layout of the LHC and the particle detectors along it (from [26]) and (b) the LHC’s nominal operation cycle. ATLAS and the LHC 37 (the integral of the instantaneous luminosity over time, which is a measure of the size of the dataset) delivered by the LHC to the different experiments in 2011. The peak luminosities achieved so far, shown in Figure 2.2(b), are the result of a progressive optimisation of beam parameters as shown in Tables 2.1 and 2.3. There are limitations, however, in how much the integrated luminosity can be optimised. Some limitations are intrinsic to the LHC design and beam, e.g. the beam optics, magnets and vacuum systems performance, the vacuum degradation due to the beam presence, the beam long-range interactions, etc. Other limitations are related rather to the LHC operation – problems may be encountered at different stages of the cycle of Figure 2.1(b). A common problem for example has been unexpected “beam dumps”, caused by “UFOs” (Unidentified Falling Objects), “SEUs” (Single Event Upsets) and overheating of the magnet system, amongst others. To illustrate this, Figure 2.3 shows the amount of time typically taken by each of the LHC operation stages. As for the optimisation of the recorded luminosity, this depends instead on to the performance of the LHC experiments and will be discussed for the case of ATLAS in Section 2.2.4. (a) (b) Figure 2.2.: Cumulative (a) and peak (b) luminosities versus day during stable beams delivered by the LHC to the experiments in 2011, from [34]. 38 ATLAS and the LHC Figure 2.3.: A pie chart of the LHC performance in 2011. The machine setup appears to take the longest, followed by the beam injection which roughly equals the time taken to recover from problems in operation and technical stops. Stable beams have been on only for about a quarter of the total operation time (from [27]). ATLAS and the LHC 39 Date Event Sep 2008 First beam circulations halted by a destructive magnetic quench (S34 incident) Oct 2008 - Recovered from “S34 incident” Oct 2009 Nov 2009 Circulating beam commissioning is resumed Dec 2009 First pp collisions at the injection energy (450 GeV/beam), subsequently reaching 1.18 TeV/beam Dec 2009- Christmas shutdown. Feb 2009 Mar 2010 First pp collisions at 3.5 TeV/beam. Oct 2010 Operation with β? = 3.5 m, 150 ns, nb = 368, L > 1032cm−2s−1. End of 2010 pp run achieving ∼ 45pb−1 of recorded data. Nov 2010 Start of the heavy ion run. Dec 2010 End of heavy ion run and Christmas shutdown. Mar 2011 Beginning of the 2011 pp run at 3.5 TeV/beam, with 75 ns. Apr 2011 Bunch spacing decreased to 50 ns. The LHC surpasses the record peak luminosity from the Tevatron. Jun 2011 ATLAS and CMS reach ∼ 1fb−1 of recorded data (2011 target), Aug 2011 β? = 1.5 m, 50 ns, nb = 1380, L > 1033cm−2s−1 Sep 2011 Technical stop. β? = 1.0 m Oct 2011 End of 2011 pp run achieving ∼ 5 fb−1 of delivered data. Table 2.2.: LHC timeline since the first beam circulation in 2008 until the end of the 2011 pp run. Numerical values are taken from [27]. Fill number Date Bunch spacing nb Peak L Nb per beam (ns) (1033cm−2s−1) (1014) 1635 18 Mar 2011 75 32 0.030 0.038 1645 22 Mar 2011 75 200 0.252 0.243 1712 15 Apr 2011 50 228 0.237 0.285 1749 30 Apr 2011 50 624 0.716 0.756 1815 29 May 2011 50 1092 1.268 1.330 Table 2.3.: Example LHC peak luminosity performances resulting from different beam parame- ters, from [27] 40 ATLAS and the LHC 2.2. The ATLAS Detector 2.2.1. Coordinate System and Kinematic Variables ATLAS has a right-handed coordinate system, as shown in Figure 2.4(a). The origin (centre of detector) is at the IP; the x-axis points towards the centre of the LHC ring, the y-axis upwards and the z-axis along the beam pipe. Cylindrical coordinates (r, φ) are used in the transverse plane (φ being the azimuthal angle around the beam pipe). As discussed in Section 1.1.2, in a hadron collider the partons of the incoming beams do not have a fixed momentum but rather a spectrum described by the PDFs. The overall process is relativistic and the centre of mass of the parton-parton scattering is normally boosted with respect to that of the parent hadrons. It is therefore convenient to describe the final state by variables which transform simply under Lorentz boosts. For this purpose, the variables used are the rapidity y, transverse momentum pT and azimuthal angle φ. In terms of these variables, the four-momentum of a particle may be written as pµ = (E, px, py, pz) (2.3) = (mT cosh y, pT sinφ, pT cosφ,mT sinh y) (2.4) where the transverse mass is mT = √ p2T +m 2. The rapidity, defined as y = 1 2 ln [ E + pz E − pz ] (2.5) has the nice property of being additive under boosts (a class of Lorentz transformations) along the z-direction and differences in rapidity are also boost-invariant. In the ultra- relativistic limit (m→ 0) the rapidity equals the pseudorapidity η: η = − ln tan(θ/2) (2.6) In ATLAS it is experimentally more convenient to use η since the polar angle θ from the beam direction is measured directly in the detector. It is also standard to use the transverse energy, ET = E sin θ (2.7) ATLAS and the LHC 41 rather than pT, since the former is what is actually measured in the ATLAS calorimeters (see Section 2.2.5). In the η-φ plane, the variable ∆R, ∆R = √ (∆η)2 + (∆φ)2 (2.8) is often used to define separation distances between physics objects (see Section 2.2.5). In ATLAS the collisions are practically head-on2, so for each event, an unknown proportion of the energy from the incoming protons escapes along the beam-pipe and if “invisible” particles (those not possible to detect with ATLAS) are created in the final state, their net momentum can only be constrained in the transverse (x-y) plane by defining a missing transverse-energy vector EmissT , which at a basic level is defined as: EmissT = − ∑ i pT(i) (2.9) where the sum runs over the transverse momentum pT (pT = p/ cosh η = p sin θ) of all visible final state particles; however the actual EmissT definitions typically implemented in ATLAS are more complicated than this (see for example Section 2.2.5). All other transverse variables are similarly defined with respect to this plane. 2.2.2. Detector Components ATLAS is a hybrid system of detectors with different technologies to be able to detect and measure different particles. It has four major systems, each of which is divided into sub-systems, arranged concentrically in a cylindrical structure, as shown in Figure 2.5. The low-η central region of these components are termed “barrel” (B) regions, whilst the high-η forward regions are referred as the “end-caps” (EC). Despite ATLAS having a nearly 4pi coverage in solid angle as a whole, the particle acceptance is limited by the geometry of its subsystems as outlined in Table 2.4. A description of each of the subsystems now follows. 2The beams meet in ATLAS at a half crossing angle of ∼ 142.5 µrad [26]. 42 ATLAS and the LHC (a) (b) Figure 2.4.: Plan views of ATLAS showing the (a) x, y, z and (b) r, η coordinates (from [35] and [36]). The general tilt of the LHC tunnel causes the y-axis to be slightly different from the vertical while high |η| values refer to regions of the detector close to the beam pipe. ATLAS and the LHC 43 Figure 2.5.: Computer generated image illustrating the different components of the ATLAS detector, from [37]. System Subsystem |η| Acceptance Design Barrel Endcap Overall resolution ID Pixel < 2.5 1.7-2.5 < 2.5 σpT/pT = 0.05%pT ⊕ 1% SCT < 1.4 1.4-2.5 TRT < 0.7 0.7-2.5 Calorimeters Presampler < 1.52 1.5− 1.8 < 1.8 - ECAL < 1.475 1.375− 3.2 < 3.2 σE/E = 10%/ √ E ⊕ 1.2% HCAL Tile < 1.0 0.8-1.7 < 4.9 σE/E = 50%/ √ E ⊕ 3% HCAL LAr 1.5-3.2 Forward 3.1-4.9 σE/E = 100%/ √ E ⊕ 10% MS Tracking < 1.0 1.4-2.7 < 2.7 σpT/pT = 10% at 1 TeV. Trigger < 2.4 Magnets Toroid < 1.3 1.6-2.7 < 2.7 - Solenoid < 2.5 < 2.5 Table 2.4.: Design acceptance [28] and resolution [36] of ATLAS subsystems. The energy resolution is parametrized as σE/E = (a/ √ E) ⊕ c, where a is the sampling term and c the constant term. 44 ATLAS and the LHC Inner Detector The Inner Detector (ID) is the tracking system. It specialises in the reconstruction of charged particle tracks and vertices, as well as measuring momentum. It is crucial to measure the impact parameter of short-lived particles (e.g B hadrons and τ leptons). It uses a combination of three subsystems, which, in order from closest to furthest from the IP are: • Pixel subdetector - made of semiconductor (Si) pixels, it has the highest resolution and it provides 3 precision measurements per track. The innermost layer (termed the “b-layer”) provides precision vertexing, which is crucial, e.g. for b-quark tagging and photon conversions identification. • Semiconductor Tracker (SCT) - made of silicon microstrips, it provides 8 precision measurements per track. • Transition Radiation Tracker (TRT) - made of straw tubes filled mainly with Xe gas, it provides 36 additional measurements per track and additional discrimination between electrons and hadrons, via the detection of X-rays produced by transition radiation. Lastly, a superconducting central solenoid (CS) magnet wraps the ID to provide a bending magnetic field (∼ 2 T). Calorimeters After the ID and CS, the system of electromagnetic (EM) and hadronic calorimeters follows (see Figure 2.5), which is of particular importance in this thesis to understand the measurements of photons and jets. Recent performance results with 2010 and 2011 data can be found in [38–40] and the design report at [41]. Overall, the calorimeters provide energy measurements of particles from the electromag- netic and hadronic showers they generate as they traverse their material, with a resolution which improves with energy (the resolution of ATLAS calorimeters is quoted in Table 2.4). High-energy electrons and photons predominantly lose energy from their electromagnetic interactions with matter (e.g. bremsstrahlung e → γe and pair production γ → e+e− respectively), which are characterised by narrow showers in ATLAS EM calorimeter (ECAL), as exemplified in Figure 2.12(a). In contrast, jets (hadrons) typically produce ATLAS and the LHC 45 a broader energy deposit from their strong interactions with the calorimeter material, with significant leakage into the hadronic calorimeter (HCAL). The amount of material traversed by the showers is measured longitudinally in terms of radiation lengths χ0 (EM case) and nuclear interaction lengths (hadronic case). In order from innermost to outermost, the calorimeter system of ATLAS is composed of the following: Presampler - consists of a thin liquid argon (LAr) layer which corrects for energy loss in the material before the calorimeters. EM Calorimeter (ECAL) - consists of a sampling calorimeter of lead and LAr with an accordion geometry (to prevent cracks). Figure 2.6 shows a sketch of one of the barrel modules, where it can be seen it consists of three longitudinal layers, in order of decreasing granularity: “Layer 1” (|η| < 1.4, 1.5 < |η| < 2.4) segmented into high granularity strips in the η direction to discriminate EM objects from hadrons; “Layer 2”, with a thickness of several χ0 to collect most of the energy from the EM showers, and “Layer 3” to correct leakage beyond the ECAL from high-energy showers. Hadronic Calorimeter (HCAL) - consists of an iron-scintillator tile calorimeter in the range |η| < 1.7 and two copper-LAr end-cap calorimeters (1.5 < |η| < 3.2). The acceptance is further extended up to |η| < 4.9 by two tungsten-LAr forward calorimeters. Magnet System The system of superconducting magnets (kept at temperatures of ∼ 4.8 K) consists of two subsystems: a thin central solenoid, already mentioned, that provides a magnetic field of ∼ 2 T to the ID; and three air-core toroids (one barrel “BT” and two end-caps “ECT”) that provide the magnetic field to the muon spectrometer. Muon Spectrometer (MS) This system specialises in stand-alone triggering and momentum measurement of muons. The direction of the magnetic field from the toroid magnet system is largely perpendicular to the muon trajectory to exert the maximum bending force. Precision measurements of the tracks are given by the Monitored Drift Tubes (MDTs), while the larger pseudora- 46 ATLAS and the LHC ∆ϕ = 0.0245 ∆η = 0.02537.5mm/8 = 4.69 mm ∆η = 0.0031 ∆ϕ=0.0245x4 36.8mmx4 =147.3mm Trigger Tower TriggerTower∆ϕ = 0.0982 ∆η = 0.1 16X0 4.3X0 2X0 15 00 m m 47 0 m m η ϕ η = 0 Strip towers in Sampling 1 Square towers in Sampling 2 1.7X0 Towers in Sampling 3 ∆ϕ×∆η = 0.0245×0.05 Figure 2.6.: Sketch of a barrel module from ATLAS ECAL, from [36]. The three layers are visible. The granularity in η and φ of the cells in each layer and of the trigger towers is also shown. ATLAS and the LHC 47 pidities are served by the Cathode Strip Chambers (CSCs) of higher-granularity. The independent trigger system is served by Resisitive Plate Chambers (RPCs) in the barrel and ThinGap Chambers (TGCs) in the end-caps. Full details of the MS can be found in [42]. 2.2.3. Trigger The trigger system in ATLAS is designed to reduce the event rate from the LHC design bunch-crossing rate (∼ 40 MHz) to a more manageable recording rate of ∼ 200 Hz. It is composed of three levels, as illustrated in Figure 2.7, to sequentially improve the decision of keeping or rejecting events. Level-1 (L1) is hardware-based and makes the first decision in < 2.5 µs by using information from the calorimeter and muon systems. It also provides Regions of Interest (RoIs) – regions of the detector potentially containing physics objects, like µ, e, γ, jets and EmissT – for the subsequent trigger levels. The other two levels are the Level-2 (L2) and the Event Filter (EF). Collectively known as the High Level Trigger (HLT), they are software-based triggers that consider the decision more carefully by accessing more event information. Limits on the output bandwidth for the three levels are set by the “trigger menu” - a programmable list of selection criteria (thresholds) to define trigger decisions. The menu has to be constantly redefined to cope with the increasing LHC luminosities. Hence, some large-output triggers need to be “prescaled”, meaning that a reduction factor is applied on the fraction of accepted events. An example of this is shown in Figure 2.8. In this thesis, the main triggers used are single-photon triggers, such as those shown in Table 2.5. As will be noted in Section 5.3.2, different triggers were used to guarantee an unprescaled trigger throughout the dataset being analysed. In general, the L1 trigger is able to compute the transverse energy of electromagnetic clusters. The photon identification is then done at the HLT, using similar variables to those used offline for identification and isolation (see Section 2.2.5 and more details in [43]). The photon triggers are typically labelled by their ET threshold and type of identification requirement (loose and tight being the most common). 48 ATLAS and the LHC LEVEL 2 TRIGGER LEVEL 1 TRIGGER CALO MUON TRACKING Event builder Pipeline memories Derandomizers Readout buffers (ROBs) EVENT FILTER Bunch crossing rate 40 MHz < 75 (100) kHz ~ 1 kHz ~ 100 Hz Interaction rate ~1 GHz Regions of Interest Readout drivers(RODs) Full-event buffers and processor sub-farms Data recording Figure 2.7.: Diagram of ATLAS Trigger/DAQ system [28]. If an event is accepted by the L1 trigger, the data is piped to the Readout Drivers (RODs) and then the Readout Subsystem (ROS). Events subsequently selected by L2 are transferred to the event-builder, after which the Event Filter can make the final decision to record the event. Luminosity block number 0 100 200 300 400 500 600 700 800 900 Tr ig ge r r at e [H z] 1 10 210 310 L2_vtxbeamspot_activeTE_peb Input rate Prescale factor Output rate 67 53 40 25 Figure 2.8.: Adjustment of the L2 trigger output rate for an arbitrary trigger menu by setting prescale factors. The “Luminosity block number” on the x-axis represents a time unit used in ATLAS. From [44]. ATLAS and the LHC 49 Trigger Offline ET cut Efficiency g20 loose 25 GeV 99.13+0.20−0.30 g60 loose 65 GeV 99.7+0.09−0.1 g80 loose 85 GeV 100+0−3 Table 2.5.: Examples of the photon triggers used and their estimated efficiencies. Uncertainties are statistical only. In the trigger name, “g” is for “gamma”, the number represents the ET threshold and “loose” the type of ID requirement. From [43]. 50 ATLAS and the LHC 2.2.4. Performance Of the total luminosity delivered by the LHC to ATLAS, ∼ 94% has been recorded, as shown in Figure 2.9. Indeed, all subsystems have been close to 100% efficient, as shown in Table 2.10. Day in 2011 28/02 30/04 30/06 30/08 31/10 ] - 1 To ta l I n te gr a te d Lu m in os ity [fb 0 1 2 3 4 5 6 7 = 7 TeVs ATLAS Online Luminosity LHC Delivered ATLAS Recorded -1Total Delivered: 5.61 fb -1Total Recorded: 5.25 fb Figure 2.9.: Cumulative luminosity versus day delivered to (green), and recorded by ATLAS (yellow) in the 2011 p-p run (from [13]). The luminosity is determined in ATLAS from “van- der-Meer scans”, where the two beams are scanned against each other in the horizontal and vertical planes to measure their overlap function. Figure 2.10.: Luminosity weighted relative fraction of good quality data delivery by the various ATLAS subsystems between March 13th and October 30th, corresponding to the 2011 recorded dataset (from [13]). ATLAS and the LHC 51 Pileup Dealing with pileup is a major experimental challenge for experiments at hadron colliders like the LHC as the beam has a bunch structure. In this context, pileup refers to the cases where more than one inelastic pp collision per bunch crossing happens inside the detector. Pileup can be “in-time” if it is caused by the IP bunch crossing or “out-of- time” if it is caused by neighbouring bunch crossings. For 2010 data, the number of reconstructed vertices nvtx was considered a good measure of the amount of pileup in the event. Currently, a more refined procedure based on the mean number of pileup interactions (or equivalently, the mean of the poisson distribution on the number of interactions per crossing) 〈µ〉 is used instead (applicable to 2011 data). It is calculated from the instantaneous luminosity as: 〈µ〉 = L σinel nbfr (2.10) where nb is the number of bunches per beam, fr is the machine revolution frequency and σinel the total inelastic pp cross-section, which for √ s = 7 TeV is ∼ 71.5 mb [13,45]. Therefore, using the LHC design beam parameters from Table 2.1, 〈µ〉 ∼ 19. However, the actual average for 2011, prior the September 2011 technical stop when β? was reduced from 1.5 m to 1.0 m (see Table 2.2), was ∼ 6.3 as shown in Figure 2.11(a). Equation (2.10) clearly states that pileup increases with luminosity, so this is an increas- ingly important matter to consider in the physics analyses of ATLAS as its impact on the results can be significant. For example, there is a significant impact on track recon- struction, simply because tracks are more difficult to reconstruct in a busy environment and selecting the correct primary vertex becomes more challenging. As will be shown in Chapter 5 and Appendix C, the comparisons of data with theory from Monte Carlo simulation can also be affected, and since the real pileup conditions change constantly, this cannot be implemented in the MC production accurately nor immediately. An event display of the typical pileup environment after β? was reduced to 1 m is shown in Figure 2.11(b) for a Z → µµ candidate event. 52 ATLAS and the LHC Mean Number of Interactions per Crossing 0 2 4 6 8 10 12 14 16 18 20 22 24 ] - 1 R ec or de d Lu m in os ity [p b -310 -210 -110 1 10 210 310 410 =7 TeVsATLAS Online 2011, -1 Ldt=5.2 fb∫ > = 11.6µ * = 1.0 m, <β > = 6.3µ * = 1.5 m, <β (a) (b) Figure 2.11.: (a) Luminosity-weighted distribution of the mean number of interactions per crossing for 2011, for data taken before and after the September technical stop, when β? was reduced. The entries at µ ∼ 0 arise from pilot bunches that were present during many of the early LHC fills (the luminosity in these is significantly smaller than in the main bunches). (b) Event display illustrating a high pileup scenario (20 reconstructed vertices) in a Z → µµ candidate event. Both figures are from [13]. ATLAS and the LHC 53 2.2.5. Physics Object Definition For physics objects to be defined for the purpose of physics analysis, the following procedures follow: i. Reconstruction: this is the process whereby the raw data digits, such as times and voltages, and other signals from the hardware in the detector are reconstructed into tracks and energy deposits to deduce the physics of the event, e.g. the track particles must have followed and their four-momenta. ii. Identification: this is the process whereby, based on certain criteria, the recon- structed tracks, energies and their profiles (e.g. shower shapes) are used to define particle candidates or physics objects like photons, electrons, muons, jets and EmissT . iii. Other Requirements: The above can be regarded as the basic requirements for object definition but, in general, each physics analysis sets their own additional criteria as a further refinement of the object. Examples of these requirements are the energy scale, quality, acceptance, isolation, overlap removal, etc. Depending on the purpose of the analysis, the criteria for some objects might be looser or tighter, e.g. a photon cross-section measurement might require a more precise definition of photons than say, a Z → ee measurement. A general summary for the above points that characterise the main physics objects in ATLAS, and which are mainly referred to in this thesis now follows (other object definitions, e.g. for b-jets, taus, etc. can be found in other references like [39,46]). Photons i. Reconstruction: Photon candidates are formed from clusters of energy deposits reconstructed in the ECAL with ET > 2.5 GeV (above the electronic noise level, which typically is < 1 GeV [36]). An algorithm attempts to match these clusters to tracks reconstructed in the ID. Clusters without matching tracks are classified as unconverted photon candidates, while clusters with matched tracks are considered electron candidates. Hence, to recover photons from conversions, clusters matched to pairs of tracks originating from reconstructed conversion vertices in the ID are considered converted photon candidates. To increase the reconstruction efficiency of converted photons, conversion candidates where only one of the two tracks is reconstructed (and does not have any hit in the b-layer, see Section 2.2.2) are also 54 ATLAS and the LHC retained [47]. The final energy measurement is made with the ECAL, in a cluster size that depends on whether the photon is converted or unconverted. A specific energy calibration is then applied separately to account for upstream energy loss in front of the ECAL (see “Calorimeter Presampler” in Section 2.2.2) and both lateral and longitudinal leakage. Clusters are removed if their barycenter lies in the transition between the Barrel and Endcap regions of the ECAL (also known as the “crack” region, corresponding to 1.37 < |η| < 1.52, see Table 2.4), where larger uncertainties related to efficiency measurements are expected. Similarly, clusters containing cells overlapping with problematic regions of the calorimeter readout or with very noisy cells are also removed. ii. Identification: Shape variables computed from the lateral and longitudinal energy profiles of the electromagnetic shower in the ECAL are used to discriminate signal from background. The definitions of these variables can be found in [48] and examples are shown in Figure C.3. Different selection criteria with respect to these variables are applied to determine the photon identification, e.g. “loose” or “tight” (see Section 5.3.1 and more details in [48,49]). The criteria do not depend on the candidate’s ET but on its pseudorapidity η (to take into account variations in the thickness of the upstream material and in the calorimeter geometry). True prompt photons are expected to have small hadronic leakage (typically below 1-2%) and narrow shower profiles, with respect to background candidates, e.g. from jets or pi0, as exemplified in Figure 2.12. iii. Other Requirements: The main other requirement for photons is isolation, which further suppresses the main background from pi0 (or other neutral hadrons decaying to γγ). The experimental isolation requirement is based on the energy deposited in the calorimeters (ECAL and HCAL) in a cone of radius ∆R = √ (∆η)2 + (∆φ)2 around the photon candidate. In order to make the measurement of EisoT directly comparable to parton-level theoretical predictions, a few corrections, obtained from simulation, are made to remove the energy of the photon itself that leaks into the isolation cone and to subtract the estimated contributions from the underlying event and pileup. After this subtraction, the remaining fluctuations are dominated by electronic noise from the calorimeter measurement. Additional details on EisoT can be found in [48,49]. Apart from isolation, other requirements are normally applied on photons, such as on the energy scale, quality, and acceptance (see Section 5.3.1). ATLAS and the LHC 55 (a) (b) Figure 2.12.: Event display of (a) a prompt photon candidate (ET = 32 GeV and EisoT = 178 MeV) and (b) a pi0 candidate (ET = 21 GeV and E iso T = 6.2 GeV) in ATLAS ECAL, from [50]. In “Layer 1”, the photon shows one peak and a narrow shower, while the pi0 shows two peaks from its decay into γγ and hence a broader profile. Electrons Being also an “egamma” object, the procedures to define electrons are, to a general level, very similar to those for photons. However, some important differences are that in the reconstruction the electron candidates are always associated to energy clusters with matched ID tracks, and losses from bremsstrahlung must be considered. As for identification, this is based on track-cluster matching and the use of the TRT subdetector (see Section 2.2.2) to further aid in the discrimination against photon conversions and charged hadrons over a wide energy range (between 0.5 and 100 GeV) [47]. Muons i. Reconstruction: Muons as reconstructed by an algorithm which looks for stand- alone tracks in the ID and the MS, which are then combined using a chi-square matching procedure [51]. ii. Identification: Two types of muons are generally used: “combined” muons are made from tracks that have been independently reconstructed in both the MS and 56 ATLAS and the LHC ID with the “STACO” algorithm, while “segment-tagged” muons use the MS to tag ID tracks as muons, without requiring a fully reconstructed MS track [51]. iii. Other Requirements: Usually muons are required to fulfil acceptance, quality and isolation requirements, e.g. for isolation, ∑ pT(tracks) in a cone of ∆R < 0.2 must be less than 1.8 GeV. Jets i. Reconstruction: Jet candidates are reconstructed from topological clusters (built from calorimeter cells) which attempt to reconstruct the three-dimensional shower topology of each particle. ii. Identification: The algorithm most commonly used in ATLAS currently is the infrared and collinear-safe “anti-kT”, with a distance parameter of R = 0.4 [52] (however, other alternatives like cone algorithms, have been used in the past). The jet four-momenta are constructed from a sum over their constituents, treating each as an (E,p) four-vector of zero mass. iii. Other Requirements: The measured jet pT, as determined at the electromagnetic scale, systematically underestimates that of the hadron-level jet and is mainly due to the non-compensating nature of the calorimeter (lower response to hadrons than electrons or photons) and the presence of dead material. Hence, an average correction, determined as a function of jet-pT and η, extracted from MC simulation is normally applied. This calibration procedure is known as “Jet Numerical Inversion Correction” and is what determines the Jet Energy Scale (JES). In addition, the Jet Energy Resolution (JER) in data is matched by “smearing” the MC. Other requirements typically applied are on the acceptance, overlap removal (wrt other physics objects, see below) and quality. Missing Transverse Energy This is determined offline with an object-based algorithm from all measured and identified physics objects, as well as any remaining energy deposits in the calorimeter. An example algorithm is MET Simplified20 RefFinal (used also in this analysis, see Section 5.4.1), where the energy clusters are associated to high-pT objects in the following order: electrons, jets and muons; and any remaining clusters are included in a so-called “CellOut” term. ATLAS and the LHC 57 The EmissT is therefore given by the following formula: (EmissT ) RefFinal x(y) = (E miss T ) RefEle x(y) + (E miss T ) RefJet x(y) + (E miss T ) RefMuo x(y) + (E miss T ) CellOut x(y) , (2.11) where each term is computed from the negative of the sum of calibrated cluster energies inside the corresponding objects. The physics objects used for Equation (2.11) must have passed some criteria like the ones defined above (full details can be found in [53]). Overlap Removal When candidates passing the object definitions overlap with each other (definition-wise), a classification is required to remove all but one of the overlapping objects. All overlap criteria are based on the simple geometric variable ∆R = √ ∆φ2 + ∆η2, based on previous studies [46]. They are generally applied in the following order: 1. If an electron and a jet are found within ∆R < 0.2, the object is interpreted as an electron and the overlapping jet is ignored. 2. If a muon and a jet are found within ∆R < 0.4, the object is treated as a jet and the muon is ignored. 3. If an electron and a jet are found within 0.2 ≤ ∆R < 0.4, the object is interpreted as a jet and the nearby electron is ignored. 58 Part II. Estimation of the Z → νν background to New Physics searches in ATLAS 59 Chapter 3. Introduction Having covered the necessary theoretical and experimental foundation in the first part, this second part presents the main work carried out both theoretically and experimentally in three chapters: Chapter 3 (this chapter) serves as the formal introduction and motivation to the main subject of the thesis. Chapter 4 then follows to present the Theoretical Studies, and Chapter 5 the Experimental Studies. For this chapter, the introduction starts with Section 3.1 where the idea of using exper- imentally simpler processes, like prompt photon production, to calibrate experimentally- harder processes, like Z boson production is posed. Section 3.2 then follows to explicitly outline the experimental challenges involved when it comes to measurements of the Z boson decaying to neutrinos (Zνν) and their importance for background estimates in Beyond the Standard Model (BSM) searches. In Section 3.3, the motivation for specifically choosing γ + jets events to calibrate Z boson production is given. Finally, Section 3.4 summarises ZfromGamma- the method/algorithm designed for this purpose. 3.1. Calibrating physics processes via cross-section ratios Given two processes A and B and their differential cross sections dσ/dx versus some observable x, we define the cross section ratio RA/B(x) simply to be the ratio: RA/B(x) = dσ(A)/dx dσ(B)/dx . (3.1) 61 62 Introduction Henceforth the A/B subscript and the argument x, are only printed as required by context. As an alternative shorthand, the notation A/B may be used when the processes are of primary concern rather than the ratio itself. If the two processes are kinematically similar in some regime, then the cross section ratio may have various nice properties, such as a relatively simple functional form (which may be approximately constant), cancellation of uncertainties and minimal dependence on other parameters. Ratios are hence of great utility within experimental analyses, with applications such as: 1. To estimate experimentally difficult Standard Model (SM) backgrounds to new physics searches by using experimentally easier processes. Their theoretical ratio R can be used to translate between the two processes, as has been done for the Zνν+jets and W`ν+jets backgrounds via the Zνν/γ, Zνν/Z`` and W/Z`` ratios[54,55]. An astute choice for the calibrating process can minimise statistical uncertainties, e.g. when estimating Z boson using W boson and photon measurements [56]. 2. To make precision measurements of SM physics (focusing in regions of phase space where new physics is not expected or has been excluded by other searches), e.g. the W/Z ratio measurement [57]. This is facilitated by the cancellation of systematic uncertainties associated to the individual cross sections in the numerator and denominator. 3. To cross-check direct cross section measurements of one process with respect to another similar process, e.g. various flavours of leptonic Z boson decays, Z`` (` = e, µ, τ). 4. Conversely to point 2 above, to test for signs of new physics (focusing in the unexplored regions of phase space). The precision of these measurements is well suited to detecting discrepancies with the SM predictions. This thesis is primarily concerned with addressing point 1 above, with points 2 and 3 being complementary aspects of the method to be discussed. Specifically, it covers a method in which Z boson production is regarded as the experimentally difficult process and photon production as the calibrating process (the reasons to choose photons will be discussed in Section 3.3). The power of the method is illustrated by calibrating the most experimentally challenging manifestation of the Z boson: where it decays to a pair of invisible neutrinos (Zνν). This forms a particular important background to Beyond-the- Standard-Model (BSM) searches targeting EmissT signatures. Its application to and results Introduction 63 for one such search, namely the ATLAS SUSY search for squarks and gluinos in the “zero lepton” channel (here abbreviated as 0` where ` = e, µ, see Section 1.2.3) [54,58] are presented. However, the generality of the method means that it can be adapted to any suitable BSM search or used for other purposes, e.g. for points 3 and 4 above, so this thesis is intended to serve as a general “manual” for estimating/calibrating Z boson rates from photon events. 3.2. The challenging Zνν background When searching for BSM signals (S), the SM processes become a background (B). The predominant search strategy (Section 1.2.3) has been to test the data for an excess of events above the SM expectation. Although different significance tests exist to resolve new signals, they all require first the determination of the total background with sufficient precision. Fundamental to this strategy is also to perform the search in regions of phase-space optimised for discovery (event selections characterised by a large S/B yield), referred to as Signal Regions (SRs). However, the disparity between BSM and most SM cross-sections means that even in the SRs the SM backgrounds can contribute significantly to the event counts in the presence of signal. Such arguments motivate the dedicated background studies in ATLAS such as the one presented here. The Zνν background is experimentally challenging for the 0` search mainly because of the following reasons: • Invisible neutrinos: The complication when invisible particles are produced in the final-state of an event is that the individual values of their energy-momentum vectors are unknown. From momentum conservation along the transverse plane (see Section 2.2.1), it is only possible to obtain a total EmissT vector (− ∑ i piT), which includes all sources of transverse momentum imbalance in the event (true and fake): EmissT =E true T +E fake T (3.2) The only expected sources of true EmissT (E true T ) from SM processes are neutrinos, which at the LHC are mostly produced in the leptonic decays of the weak bosons W → `ν (∼ 22%), Z(→ νν) (∼ 20%) and heavy-flavour quarks b→ `ν (∼ 11% [5]). However, a fake component (EfakeT ) is also expected due to experimental effects, e.g. systematic errors like jet mismeasurements or non-collision backgrounds like 64 Introduction cosmic rays. The key point is that it is not possible to tell apart the different components. • Irreducibility: A background becomes irreducible if it has exactly the same final- state as the targeted signature in the BSM search, making it impossible, even in a perfect detector, to entirely eliminate its contribution from the total event count. Only an estimate for it can be made. Consequently, irreducible backgrounds tend to be amongst the most dominant contributions to the total background. Clearly, for all BSM searches involving EmissT + jets and no leptons, like the 0` search, Zνν is the irreducible SM background – Zνν events typically pass the SR selections due to the invisible Z recoiling with large pT against the hadronic activity to produce substantial true EmissT . One potential source of estimates for SM backgrounds is of course Monte Carlo (MC) simulation. But, despite the sophistication and versatility of MC event generators nowadays, there remain technical and theoretical limitations, e.g. calculation of multileg matrix-elements and their use in simulation of SM background events to new physics searches. Various examples of disagreement between data and simulation demonstrate the pitfalls of relying only on limited matrix-elements and parton showering when probing extreme regions of phase space, e.g. those involving multijets and EmissT [59]. It is hence essential to use data-driven methods, i.e. those that extract background estimates from data instead of purely from simulation. How much the method relies on data may be to a greater or lesser extent, e.g. the data may be used purely for normalisation, but it may also drive other details of the estimate. Insofar as the method to be discussed here makes use of MC to some extent, e.g. to determine the cross section ratio RZ/γ, it can be considered as rather partially data-driven. 3.3. Using γ events to calibrate Z boson normalisation It is most straightforward to choose the calibration process to be as similar as possible to the process to be estimated. In principle, for Zνν + jets the first such option would be Z`` + jets (` = e, µ). Being a well-understood process that can be cleanly measured, by treating the lepton pair momentum as an estimator of the true EmissT , an event sample of pseudo-Zνν + jets events can be produced, where the theoretical cross section ratio only Introduction 65 differs by the branching ratio. In practice, however, the number of Z`` + jets events in control samples tends be too small to do this with sufficient precision (Br(Z``) ∼ 6.7% versus Br(Zνν) ∼ 20%). Indeed, the smallest theoretical uncertainty is expected from using Z`` (∼ 0.01% [60]), but the fundamental problem is that the poor statistics of this process could lead to quite the opposite, e.g. by requiring extrapolations from looser to harder selections (as has been done in the 0` search for this calibrating process [54]). The next option would be to use the other weak boson, W`ν , but in this case the modest gain in statistics with respect to Z`` is counteracted by larger theoretical uncertainties with respect to Zνν and reduced purity in the experimental event selection. But one vector boson remains: the photon γ. Having a much higher production rate with respect to Z`` and W`ν (there is no branching ratio suppression for photon production), as shown in Figure 3.1(a), it offers the best statistics, and thus is a good alternative as long as the theoretical uncertainties can be kept at a competitive level. As will be shown in Chapter 4 and Section 5.5.3, and illustrated in Figure 3.1(b), the Z boson and γ production processes become very similar at high boson pT (pT  mZ). At this point, the only expected difference in rate comes from their electroweak couplings to quarks, which are very well determined. Given that the Z and γ η distributions converge at high boson pT, the dependence of the cross-section ratio on the pT, RZ/γ = RZ/γ(pT) = dσ(Z + jets)/ d pT dσ(γ + jets)/ d pT (3.3) makes this a natural parameterisation for the ratio determination. The ratio will also prove to be robust with respect to both theoretical uncertainties and experimental effects, which should be similar for both processes and therefore cancel in the ratio. Furthermore, the event selections of BSM searches like 0` are characterised by high-pT requirements, where RZ/γ is relatively constant with respect to event kinematics (see Figure 3.1(b)). Therefore, given all the reasons above, it can be concluded that the measured rate of γ + jets production, coupled with theoretical knowledge of the ratio of Z and γ SM cross-sections can be used to accurately predict the Zνν background. 66 Introduction (V) (GeV) T p 100 200 300 400 500 600 700 800 Cr os s Se ct io n (pb / G eV ) -510 -410 -310 -210 -110 1 10 γ )ν νZ( )ν µW( (a) (V) (GeV) T p 0 100 200 300 400 500 600 700 800 )γ R( Z/ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 14 TeV 7 TeV PYTHIA8 (b) Figure 3.1.: (a) Differential cross section as a function of vector boson pT for the processes pp → V + X with V = Zνν ,W`ν and γ at √ s = 7 TeV based on LO V + 1 parton Matrix Elements. The γ + jets process yields the largest rate; and (b) Z/γ ratio showing the simple relationship at high pT where a plateau is reached. Both plots are from PYTHIA8. 3.4. ZfromGamma Method Overview Although theoretically only the knowledge of RZ/γ(pT) is enough to translate between the two processes, experimentally additional corrections need to be considered. The ex- perimental method suggested here will be referred throughout the thesis as “ZfromGamma” and is based on the use of a control sample (here referred to as “Control Region” CR) and a “Transfer Function” TF to make the experimental Z/γ conversion. The ZfromGamma method and its multiple applications are summarised in Figure 3.2. First, an inclusive sample of prompt photon candidate events (γ +X) are selected from data as specified in Section 5.3. At this stage, the results can be cross-checked with prompt photon cross section measurements as in references [49,61] (Appendix B). The next step depends on the process to be calibrated. For example, if aiming for an estimate of inclusive Z boson rates (Z +X), the only additional step would be to apply the Transfer Function TFZ which has the effect of converting a number of photon events Nγ to Z boson events: NZ(pT) = TFZ(pT) ·Nγ(pT) (3.4) Hence, for a given pT, TFZ can be regarded as an overall normalisation factor applied to a control sample of the chosen calibrating process to obtain an estimate for the process Introduction 67 of interest. As will be discussed later, TFZ mainly depends on the boson pT and is given by, TFZ(η, pT)→ TFZ(pT) = P (pT) Aγ(pT) · εγ(pT) ·RZ/γ(pT) (3.5) where P (pT) = (1− fbkg(pT)) is the purity of the sample; fbkg(pT) being the fraction of events other than direct photon production, i.e. the background in the photon sample (Section 5.5.2), Aγ(pT) ·εγ(pT) is a correction to account for experimental effects from the detector acceptance and reconstruction efficiency of reconstructed photons (Section 5.5.1) and RZ/γ(pT) is the cross-section ratio already discussed. A γ(pT) is by definition the fraction of the photon η distribution at a given pT that falls within the η range considered in the analysis; while εγ and P have both been shown to change little with η [49] (also see Tables B.1-B.3). So far, the conversion denoted by Equation (3.5) is agnostic in the decay modes of the Z boson, so the next branch in Figure 3.2 is to represent the possibility to specialise the TF to a particular decay mode: assuming that the Z boson decays invisibly to neutrinos, but retaining inclusiveness in the rest of the event (Zνν +X). In order to simulate the Zνν kinematics, the prompt photon γ1 has to be “neutrinofied”, meaning that its pT is treated as the true EmissT in Zνν events (“pT(γ1)→EtrueT ” in Figure 3.2). Then, the TF has to be scaled by the Zνν branching fraction (TFZνν in Figure 3.2). For an estimate of Zνν background given a tighter event selection, e.g. for a BSM search, the TF needs to be computed in a suitable Control Region (TFCRZνν in Figure 3.2), and to define the Control Region (CR) it may be sufficient to replicate the SR selection, after applying the neutrinofication step (Section 5.4). Applying TFCRZνν to the photon events selected in the CR therefore results in the Zνν + jets background estimate. This is acceptable as long as: (i) the SR selection is tighter than the γ + X sample selection, and (ii) the statistics of the γ +X sample at the SR are large enough in order to avoid extrapolations, e.g. from a looser selection. In general, both (i) and (ii) straightforwardly apply. One potential complication arises when multiple SR selections lie in kinematic regions with differing values/forms for RZ/γ(pT). In such cases, one might need to determine RZ/γ(pT) separately for each SR, or account better for the variation of the ratio with respect to other kinematic quantities. This is particularly important when aiming to minimise theoretical uncertainties. The method just described will be referred throughout this thesis simply as “ZfromGamma”. Regarding its historical background, the first developments were done by CMS in 2008[62], 68 Introduction and the first attempt to implement it in ATLAS was in 2010 for the first SUSY 0` search [63]. These results were presented at the Moriond’11 conference and hence are considered the first of their kind in ATLAS. They are summarised in Appendix C.1. However, it was only in 2011 that a robust theoretical assessment became available in two studies: Z/γ+ 2 jets NLO studies [64] and the calculation of associated uncertainties, experimental effects and robustness of the RZ/γ ratio [56]. The second of these two is what is presented in Chapter 4. The method has since become the mainstream to estimate the Zνν background in the multiple analysis rounds of the SUSY 0` search in ATLAS. In chronological order, results have been provided for the Moriond’11 [58], PLHC’11 [65], EPS’11 [54] and Moriond’12 [66] conferences, which are documented in Appendices C.1, C.2, C.3 and Chapter 5 respectively. Methods similar to this have also been implemented in other experiments like CMS (Section 6.1.1) and CDF (e.g. WW/ZZ search [67]). Introduction 69 Inclusive  Photon  Selec0on   γ+X events Z+X events Data Zvv+X events     ϒ          Z  Transfer  Func0on:               ϒ          Z  Transfer  Func0on:           BSM  SR  Selec0on   “neutrinofica0on”   pT(ϒ1)            ETtrue   ZSRvv+X events     ϒ          Z  Transfer  Func0on:           CR events Figure 3.2.: Schematic charts summarising the different applications of the ZfromGamma method and steps required for each. The leftmost part of the diagram illustrates how to get a general estimate of inclusive Z rates from inclusive γ rates; the centered and rightmost parts correspond to more specific estimates of Zνν events and Zνν + jets background in a BSM EmissT + jets search respectively. The meaning of the variables and abbreviations are specified elsewhere in the text. 70 Chapter 4. Theoretical Studies The aim of this chapter is to present the main theoretical work carried out for this thesis. This work was done in collaboration with S. Ask, M. A. Parker, M. E. Shea and W. J. Stirling from the University of Cambridge and was published in 2011 [56]. This chapter is hence merely a summary of this reference and the specific contributions from the author are specified at the end of this introduction. The motivation for these theoretical studies arose from the need to know precisely the relationship between the Z boson and γ, specifically their production cross-section ratio, in order to implement the ZfromGamma method described in Chapter 3. Moreover, it was necessary to show that this ratio was robust with respect to experimental effects and event selections for the method to be considered competitive. In addition, as pointed in Section 3.4, at the time of the first implementation there were few theoretical studies available. The structure of this chapter is as follows: Section 4.1 presents the motivation for determining the Z/γ cross-section ratio in such detail. Sections 4.2 and 4.3 present the studies of this ratio for final states involving 1, 2 and 3 hadronic jets, using both the leading–order parton shower Monte Carlo program PYTHIA8 [68] and the leading– order matrix element program GAMBOS [69]. This enabled an understanding of the underlying parton dynamics in both processes, and to quantify the theoretical systematic uncertainties in the ratio. Section 4.4 presents the extension of these parton-level studies to full event simulation and how, using a typical set of experimental cuts from an ATLAS SUSY 0` search, the net theoretical uncertainty in the ratio is estimated to be of order ±7%, while uncertainties associated with full event simulation are found to be small. Lastly, Section 4.5 presents a summary of these studies where the highlight is a quoted overall accuracy of the method, excluding statistical errors, of order 10%. 71 72 Theoretical Studies Supervised by S. Ask and M. A. Parker, the author performed most of the PYTHIA- related work and plots, specifically in Section 4.3.1 (Figures 4.4, 4.5); Section 4.3.2 (Figures 4.7, 4.8) and Section 4.3.3 (Figure 4.11); the plots in Section 4.4 were made by the author in collaboration with S. Ask and all the other plots not quoted above e.g. GAMBOS and MSTW08 related, were made by M. E. Shea and W. J. Stirling. 4.1. The Z/γ Ratio Although the Z and γ cross sections have a simple theoretical relationship at high vector boson pT , care is needed when estimating the theoretical ratio of Z and γ SM cross sections. Especially for more than one jet, there are matrix element contributions to the cross section that may not be included in parton shower Monte Carlos such as PYTHIA [68, 70] or HERWIG [71]. In addition, it is important to quantify the theoretical uncertainty on the ratio (from the choice of PDFs, QCD scales etc.), since this will propagate through to the overall uncertainty on the background estimate. A detailed theoretical study of the V+ jets (V = γ, Z) cross sections and uncertainties is therefore required, to supplement the information from Monte Carlo event simulation. Finally, it is important to establish how well the theoretical precision survives under conditions closer to the experimental analysis, e.g. including effects from full event simulation, jet reconstruction, detector acceptance, experimental cuts etc. Since our main interest is in estimating the missing ET distribution in events with multijets, we focus primarily on the inclusive vector–boson (Z or γ) transverse momentum (pT ) distributions, particularly at high pT MZ . We first analyse the ratio of the Z+1 jet and γ + 1 jet pT distributions from a general theoretical perspective using a program for up to and including 3 jets based on exact leading–order parton–level matrix elements. We then reproduce these results using PYTHIA8 [68, 70] (at parton level). This establishes that the ratio of the two process cross sections is theoretically robust, particularly at high pT . We predict the value of the cross section ratio using ‘typical’ experimental cuts, and estimate its theoretical uncertainty. We then consider the corresponding 2– and 3–jet cross sections, again comparing the exact leading–order matrix element results with those obtained from PYTHIA8. Finally, we use our results to assess the systematic uncertainties on the missing transverse energy + jets background obtained from the photon + jets cross section using this method. The ratios predicted by the two alternative approaches, based on “pure” matrix elements or parton showers, are illustrated as well as used to Theoretical Studies 73 constrain the systematic uncertainties related to the commonly used, and also more optimal, scenario where matrix elements are matched with the parton shower used in the MC simulation. In the following sections, V refers to the vector bosons Z or γ. In a recent paper [64], a similar study was carried out for the V + 2 jets cross sections using two approaches: next–to–leading order in pQCD applied at parton level, and exact leading–order matrix elements interfaced with parton showers (ME+PS) as implemented in SHERPA [72]. Agreement between our results and those of [64] confirms that over much of the relevant phase space, and particularly for inclusive quantities, the effect of higher–order corrections on the leading–order Z, γ cross section ratios is small. In our study, we consider also the 1– and 3–jet ratios and, more importantly, we extend the analysis to hadron level using PYTHIA8. This allows for an analysis similar to the ones within the LHC experiments. We also examine the dependence of the ratios on the parton distribution functions, since these receive different weightings in the Z and γ cross sections and therefore do not exactly cancel in the ratio. Of course ultimately one would wish to evaluate all these cross sections consistently at next–to–leading order, using the methods described in [64] for the 2–jet case. 4.2. V+jets production in leading–order perturbative QCD In the Standard Model, the coupling of photons and Z bosons to quarks q are, respectively, −ieQqγµ and −ie 2 sin θW cos θW γµ(vq − aqγ5), (4.1) where Qq, vq and aq, are respectively the electric, vector and axial neutral weak couplings of the quarks, and θW is the weak mixing angle. For hadron collider processes such as qq¯ → V +ng or qg → qV +(n−1)g, both of which contribute to V +n jets production, the matrix elements squared will contain factors of Q2q or (v 2 q + a 2 q)/4 sin 2 θW cos 2 θW for γ or Z respectively. The only other difference in the matrix elements comes from the non–zero Z mass1, which will appear in the internal propagators and phase space integration. Sample Feynman diagrams for V + 1 jet production are shown in figures 4.1(a,b), and for V + 2 jet production in figures 4.1(c–f). 1For the purposes of this discussion, we treat the Z as an on–shell stable particle. In practice, Z decay will also form part of the matrix elements. 74 Theoretical Studies Figure 4.1.: Sample Feynman diagrams for V + 1, 2 jets production, where V = γ, Z. For high pT (V ) ( MZ) production we would therefore expect the Z and γ cross sections to be in the ratio Rq = v2q + a 2 q 4 sin2 θW cos2 θWQ2q . (4.2) Substituting sin2 θW = 0.2315, we obtain Ru = 0.906 and Rd = 4.673. In practice, of course, the cross sections will receive contributions from all quark flavour types, and so R = σ(Z)/σ(γ) will be a weighted average of the Ru and Rd values, i.e. R = Zu〈u〉+ Zd〈d〉 γu〈u〉+ γd〈d〉 (4.3) in an obvious notation, where 〈u〉 and 〈d〉 are the typical values of the u–type and d–type quark parton distribution functions (PDFs) in the cross section. Figure 4.2(a) shows R as a function of the ratio 〈d〉/〈u〉. We would expect that where large x values are probed, for example at very high pT (V ), the ratio would approach the Ru value since Theoretical Studies 75 d(x)/u(x)→ 0 as x→ 1, e.g. suggested by Figure 4.2(b). For moderate pT values at the LHC, 〈x〉 ∼ 0.1, which corresponds to 〈d〉/〈u〉 ' 0.6 and therefore R ' 1.4. The simple connection (4.3) between the vector boson cross section ratio and the initial state quark flavour is, however, broken for njets ≥ 2. Consider for example the sample Feynman diagrams of figure 4.1(e) and (f). For the former ‘four–quark’ diagrams, the vector boson can be emitted off any of the external quark legs and so the numerator and denominator of the ratio R depend on more complicated products of quark distributions. Because at high x uu scattering will be relatively more dominant than dd scattering, we would expect that the value of R for such processes would be closer to Ru than to Rd, compared to the 1–jet ratio. On the other hand, for the gg–scattering diagrams, figure 4.1(f), the ratio of the corresponding cross sections is (ignoring the Z mass) R = ∑ q Zq/ ∑ q γq, where the sum is over the final state quark (antiquark) flavours, and the dependence on the initial state (gluon) distributions cancels. By way of illustration, with 5 massless flavours we obtain R = 1.933. As we shall see below, the four–quark contribution is more important at high pT than the gg contribution, and the net effect is to reduce R slightly compared to the 1–jet case. 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 / R (Z /γ) R(Z/γ) = (Z u +Zd)/(γu+γd) (a) 10-2 10-1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 d MSTW2008LO Q2=104 GeV2 x x f(x , Q2 ) u (b) Figure 4.2.: (a) Dependence of R = σ(Z)/σ(γ) at the coupling constant level on the ratio of average d and u parton distribution values, see eq. 4.3. (b) u and d quark MSTW2008LO PDFS [73] at Q2 = 104 GeV2. 76 Theoretical Studies Figure 4.3(a) shows the Z + 1 jet and γ + 1 jet cross sections2 as functions of the vector boson transverse momentum at √ s = 7 TeV and 14 TeV. Standard PDG values of the electroweak parameters are used, and the PDFs are the leading–order MSTW2008LO set [73] with renormalisation and factorisation scale choice µR = µF = pT (V ), and the Z is treated as an on–shell stable boson. The acceptance cuts are |y(V, j)| < 2.5 and pT (V, j) > 40 GeV, where y is the rapidity. Figure 4.3(b) shows the ratio of the Z and γ distributions. We see the expected behaviour of a roughly constant ratio at large pT (V )MZ lying between the Ru and Rd values defined above. Although above pT ∼MZ the ratio does exhibit a plateau region, at very large pT we begin to see a slight decrease, as the high–x behaviour of the d/u PDF ratio drives the ratio down towards the Ru value. At 14 TeV, the empirical large–pT value of R ' 1.4 is consistent with 〈d〉/〈u〉 ' 0.6, see figure 4.2(a). This in turn is consistent with u and d PDFs probed in the x ∼ 0.1 region, see figure 4.2(b). At the lower collider energy (7 TeV), higher x values are sampled for the same pT , and the Z/γ ratio decreases slightly, moving towards the Ru value. Note that the ratio curves in figure 4.3(b) can be reasonably well approximated by R = R0 ( p2T p2T +M 2 Z )n , (4.4) with n ≈ 1.2, illustrating the expected Z mass suppression relative to the photon distribution for pT < MZ . 4.3. Parton level analysis In order to study the ratio of the Z and γ distributions in a realistic experimental environment, we need to use an event simulation Monte Carlo program. We use PYTHIA8 for this purpose. At the same time, we want to understand the difference between the scattering amplitudes embedded in PYTHIA8 and the amplitudes obtained using exact QCD matrix elements for multijet production. For the latter we use the program GAMBOS, an adaptation of the Giele et al. Vecbos program [69] for W,Z + n jets production, in which the weak boson is replaced by a photon. First, we compare the PYTHIA8 and GAMBOS results at the parton level. This serves to check the consistency of the results from the two programs, when configured as similarly as possible, and provides a common middle step between the matrix–element (ME) 2Expressions for the matrix elements can be found, for example in Chapter 9 of [3]. Theoretical Studies 77 0 100 200 300 400 500 600 700 800 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 7 TeV γ + 1 jet Z + 1 jet pT (GeV) dσ / d p T (nb /G e V) MSTW2008LO 14 TeV (a) 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 7 TeV pT (GeV) R (Z /γ) 14 TeV (b) Figure 4.3.: (a) Z and γ pT distributions at √ s = 7 TeV and 14 TeV, with parameters and cuts as described in the text. (b) Ratio of the Z and γ pT distributions. V+ jets results at parton level produced by GAMBOS and the results for fully simulated events from PYTHIA8. The PYTHIA8 results are obtained using the LO (2 → 2) processes, qq¯ → V g and qg → V q where V = γ or Z, corresponding to the Feynman diagram types shown in figures 4.1(a,b). Events with ≥ 2 jets are generated by parton showering off the initial and final state partons. This means that processes such as those shown in figures 4.1(c) to 4.1(f) are included, albeit with an approximation to the exact matrix elements, and we can therefore expect differences between GAMBOS and PYTHIA8 results for the Z/γ ratios with ≥ 2 jets. In order to produce results directly comparable with GAMBOS, the following settings are used as default in PYTHIA8: • PDFs: MSTW2008LO; • Strong: αS(M2Z) = 0.13939, with one loop running; • EM: αEM(M2Z) = 1/127.918, with one loop running; • Weak: sin2(θW ) = 0.2315; • Scales: Renormalisation and factorisation scales, µR = µF = pT (V ); 78 Theoretical Studies • Rapidity, transverse momentum and separation cuts on the final–state Z, γ and jets as described in the previous section. In the following sub–sections we first compare results for the V + 1 jet distributions, then discuss the theoretical uncertainties on the corresponding Z/γ ratio, and finally compare the V + 2, 3 jet results from the two programs. 4.3.1. V + 1 jet results The LO matrix elements used in the PYTHIA8 processes are the same as those used in GAMBOS for the V + 1 jet case, and a parton level comparison between the two programs should therefore give identical results. Note that the V and the jet correspond to the outgoing partons of the hard process in PYTHIA8, without any further simulation of the event. The differential Z and γ cross sections and their ratio predicted by PYTHIA8 are shown in figure 4.4 for pp collisions at 7 as well as 14 TeV. The results show the same characteristic features already seen in the GAMBOS predictions in figure 4.3, i.e. the Z cross section, excluding any branching ratios, is smaller than the photon cross section at small pT due to the mass suppression, but is roughly proportional to, and slightly larger than, the γ cross section at pT  MZ . The ratios obtained from PYTHIA8 and GAMBOS are compared in figure 4.5, for 7 TeV and 14 TeV collision energies. Evidently there is good agreement between the two programs, as expected. As seen in the plot, the photon cross sections from the two programs agree perfectly, whereas a small difference between the Z cross sections, <5%, is visible. This difference is due to the way in which the PYTHIA8 generator treats the Z boson as a resonance, in contrast to GAMBOS where the Z is treated as a real particle, and this was confirmed by producing a GAMBOS like process in PYTHIA8 which reproduced the same results. Since the Z boson is generally treated as a resonance in MC programs, this difference is not considered as a source of uncertainty. 4.3.2. Theoretical uncertainties Having established numerical agreement between the two programs, we can use PYTHIA8 to investigate the theoretical uncertainty on the Z/γ ratio at high pT . There are a number of sources of these, which we address in turn. First, we consider the dependence on the PDFs used in the calculation. As argued in section 4.2, the Z/γ ratio at high pT is sensitive to the d/u parton ratio at large x. Theoretical Studies 79 (V) (GeV) T p 0 100 200 300 400 500 600 700 800 (nb /20 G eV ) T / d p σd -810 -710 -610 -510 -410 -310 -210 -110 1 10 Z + 1 jet + 1 jetγ 7 TeV 14 TeV PYTHIA8 (a) (V) (GeV) T p 0 100 200 300 400 500 600 700 800 )γ R (Z / 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 14 TeV 7 TeV PYTHIA8 (b) Figure 4.4.: (a) Differential cross section as a function of the vector boson pT for the process pp→ V + 1 parton with V = γ, Z from PYTHIA8, and (b) the ratio of these. (V) (GeV)p PY TH IA ) T /d p σ / (d G AM BO S ) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 1J 7 TeVγ Z 7 TeV 14 TeVγ Z 14 TeV (V) (GeV) T p 0 100 200 300 400 500 600 700 800 PY TH IA ) γ Z/ / (R G AM BO S ) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1J7 TeV 14 TeV Figure 4.5.: Effect on the boson pT and the ratio from using a matrix–element generator (GAMBOS) and PYTHIA8 at 7 and 14 TeV. To study the possible variation in this ratio, we investigate the spread from using the different eigenvectors of the MSTW2008LO set and we compare these predictions with those from two (older) leading–order PDF sets, CTEQ5L [74] and GRV98 [75], shown in figure 4.6. The latter should yield a conservative estimate of the PDF dependence. The 80 Theoretical Studies impact on the Z and γ distributions and their ratio is shown in figure 4.7. Note that the CTEQ5L and GRV98 PDFs give respectively softer and harder Z and γ pT distributions, which is an artefact of the underlying quark and gluon PDF behaviour, see figure 4.6(a), but that the effect largely cancels in the ratio. The residual small differences in the cross section ratio can be understood in terms of the corresponding small differences in the d/u ratio for the various sets, shown in figure 4.6(b). We ascribe a conservative ±4% PDF uncertainty to the R(Z/γ) ratio at high pT (V ). In addition to varying the PDFs, we use different choices for the renormalisation and factorisation scales, µR and µF , in order to mimic the effect of higher–order pQCD corrections not included in either the PYTHIA8 or GAMBOS analyses. In particular, we use multiples of the default scales µR = µF = pT (V ), and two variants of this: the arithmetic and geometric means of the final-state transverse masses in the 2→ 2 hard process, µ2ari = (m2T1 +m 2 T2)/2 = (2pT (V ) 2 +m(V )2)/2 and µ2geo = mT1mT2 = pT (V ) √ pT (V )2 +m(V )2. Note that for the photon, these scales are identical to the default scale pT (γ). Figure 4.8 presents the corresponding impact on the differential cross sections, dσ/dpT , as well as the cross section ratio, R(Z/γ). The results show that although the variations have significant effects on the differential cross sections, as expected, the Z/γ ratio remains stable in the regime pT MZ , and for pT (V ) > 100 GeV all variations of the ratio are within ±3%. 0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 d MSTW08 LO GRV98 LO CTEQ5L Q2 = 104 GeV2 x x f(x , Q2 ) u (a) 0.01 0.1 1 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 MSTW08 LO 68% cl errors GRV98 LO CTEQ5L Q2 = 104 GeV2 x d(x , Q2 )/u (x, Q2 ) re la tiv e to M ST W 08 (b) Figure 4.6.: (a) Comparison of up and down quark distributions from MSTW2008LO, CTEQ5L and GRV98. (b) d/u ratios compared to MSTW2008LO. Theoretical Studies 81 Indeed the only sizable effect on the ratio related to the scales is observed from the different choices of the scale µR, which becomes visible at pT  MZ . Any choice of scale of the form κpT will of course cancel in the Z/γ ratio, but scales of the form κ √ p2T +M 2 V will give different results for low pT ∼MV . The size of this effect was also shown to be consistent with the ratio αS(µR(Z))/αS(µR(γ)) using the same one–loop formula as in PYTHIA8 and GAMBOS, e.g. see Figure 4.9. No similar effects are observed from different choices of the factorisation scale µF , since the PDFs vary only weakly with the factorisation scale at the x values probed by these cross sections. Note that in the above analysis we have used the same form of scale variation simultaneously in both the numerator (Z) and denominator (γ) cross sections. As pointed out in Ref. [64], this gives a much smaller scale variation than if the scales are varied independently in the two cross sections. However, we argue that if we select Z and γ events for which the kinematics of the (colour–singlet) vector bosons and the jets are the same, and if the energies and momenta are large enough such that the Z mass can be neglected (e.g. pT MZ), then the higher–order pQCD corrections to both cross sections should essentially be the same and should therefore largely cancel in the ratio. (V) (GeV)p M ST W 08 ) T /d p σ / (d i) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 PYTHIA8 7 TeV , i=GRV98γ , i=CTEQ5Lγ Z, i=GRV98 Z, i=CTEQ5L (V) (GeV) T p 0 100 200 300 400 500 600 700 800 M ST W 08 ) γ Z/ / (R i) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 PYTHIA8 7 TeVi=GRV98 i=CTEQ5L Figure 4.7.: Effects on (Z, γ) differential cross sections and cross section ratio after varying the PDFs. 82 Theoretical Studies (V) (GeV)p 0) T /d p σ / (d i) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 PYTHIA8 7 TeV) T /2, p T , i=(pγ ) T , p T , i=(2pγ ) T /2, p T Z, i=(p ) T , p T Z, i=(2p (V) (GeV) T p 0 100 200 300 400 500 600 700 800 0) γ Z/ / (R i) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 PYTHIA8 7 TeV) T /2, p T i=(p ) T , p T i=(2p (a) (V) (GeV)p 0) T /d p σ / (d i) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 PYTHIA8 7 TeV/2) T , p T , i=(pγ ) T , 2p T , i=(pγ /2) T , p T Z, i=(p ) T ,2p T Z, i=(p (V) (GeV) T p 0 100 200 300 400 500 600 700 800 0) γ Z/ / (R i) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 PYTHIA8 7 TeV/2) T , p T i=(p ) T , 2p T i=(p (b) (V) (GeV)p 0) T /d p σ / (d i) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 PYTHIA8 7 TeV) T , pgeoµ, i=(γ ) T , p ari µ, i=(γ ) T , pgeoµZ, i=( ) T , p ari µZ, i=( (V) (GeV) T p 0 100 200 300 400 500 600 700 800 0) γ Z/ / (R i) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 PYTHIA8 7 TeV) T , pgeoµi=( ) T , p ari µi=( (c) (V) (GeV)p 0) T /d p σ / (d i) T /d p σ(d 0.8 0.9 1 1.1 1.2 1.3 1.4 PYTHIA8 7 TeV)geoµ, T, i=(pγ ) ari µ, T , i=(pγ )geoµ, TZ, i=(p ) ari µ, T Z, i=(p (V) (GeV) T p 0 100 200 300 400 500 600 700 800 0) γ Z/ / (R i) γ Z/ (R 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 PYTHIA8 7 TeV)geoµ, Ti=(p ) ari µ, T i=(p (d) Figure 4.8.: Effects on (Z, γ) differential cross sections and cross section ratio after varying the scales (µR, µF ). The different µ scales are defined in the text and the denominators correspond to using the default scale choice, i.e. 0 = (pT , pT ). 4.3.3. V + 2, 3 jets results For the V + 2 jets production cross sections there is an additional complication in that the high–pT photon can be emitted collinearly to a high–pT quark, with the transverse momentum of the pair being balanced by an ‘away side’ quark or gluon. For massless Theoretical Studies 83 [GeV] T Boson p 50 100 150 200 250 300 350 400 ) γ2 (Q S α ) / Z2 (Q S α 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 T 2 = pren 2Q of V) T 2 (mV2 + mT2 = pren 2Q T 2 = V/jet mean (Geom) mren2Q T 2 = V/jet mean (Arit) mren2Q Figure 4.9.: Expected effect on αS from using different renormalisation scales Qren in RZ/γ. The plot is obtained from a fit to the PYTHIA8 MC. photons, quarks and gluons the matrix element is singular in this configuration and so the closer the photon is allowed to approach the quark, the smaller the Z/γ ratio becomes, since there is no such collinear singularity for Z production. To regulate the singularity, we impose a ∆R(V, j) > ∆Rmin isolation cut, where V = γ, Z and j = q, g. 3 We also, of course, need to impose rapidity, transverse momentum and jet–jet separation cuts on the quark and gluon jets. For illustration, we choose pT (j) > 40 GeV, |y(j)| < 2.5 (as for the 1–jet study above), and ∆R(j, j) > 0.4 to represent ‘typical’ experimental cuts. Figure 4.10(a) shows the ratio of V + 2 jet cross sections, as calculated using GAMBOS, for different values ∆Rmin = 0.05, 0.1, 0.2, 0.4, 0.6 at 7 TeV. The ratio at high pT shows the expected dependence on the minimum separation. Note also that the ratio becomes insensitive to the isolation cut when the minimum separation becomes large, since far from the singularity the Z and γ phase space are affected more or less equally. A similar dependence on ∆Rmin is observed for the V + 3 jet ratios. From now on we take ∆Rmin = 0.4 as our default choice and attribute a ±5% uncertainty of these results based on the difference with respect to ∆Rmin = 0.6. The breakdown of the Z + 2 jet GAMBOS cross section at 7 TeV into the different subprocess contributions is shown in figure 4.10(b). We define these to be qq¯ → V gg scat- 3Note that the requirement of photon isolation becomes more subtle beyond leading order in pQCD, since in this case the partonic jets can have non–zero ‘width’ and the choice of jet algorithm influences the analysis. This issue is addressed in detail in Ref. [64]. In our case we will be studying photon isolation for the full PYTHIA8 event simulation including hadronisation and experimental cuts. Note also that we neglect contributions to the γ cross section involving photon fragmentation functions, i.e. fq→γ(z,Q2). With the strong isolation requirements and high transverse momentum values used in our study, we expect such contributions to be small. 84 Theoretical Studies tering (e.g. figure 4.1(c)), qg, gq → V qg (e.g. figure 4.1(d)), gg → V qq¯ (e.g. figure 4.1(f)) and qq → V qq (e.g. figure 4.1(e)), where a sum over quarks and antiquarks is implied. Note that quark–gluon scattering is by far the most dominant in the kinematic region studied here, and its fractional contribution is roughly independent of pT (V ). The results also show that the second largest contribution in the 2–jets case comes from the qq subprocess, which approximately amounts to 20%. This is in contrast to the 1–jet case, which is dominated by qg and qq¯ scattering. The corresponding subprocess breakdown of the γ + 2 jet cross section is similar. In figure 4.11(a) we show the Z/γ+ 1, 2, 3 jet GAMBOS cross section ratios as a function of pT (V ), with ∆Rmin = 0.4 and other cuts as before. We see that the 2,3 jet ratios are slightly smaller than the 1 jet ratio at moderate and high pT . The small difference arises from three effects: (i) the dependence of the 2,3 jet cross sections on ∆Rmin = 0.4, (ii) the additional qq and gg scattering diagrams, the net effect of which is to decrease the 2,3 jet ratio, as already explained in section 4.2, and (iii) the fact that for a fixed pT , increasing the number of jets increases the overall invariant mass of the final–state system, and also therefore the values of the parton momentum fractions. This in turn decreases the d/u ratio, and also the Z/γ ratio, see figure 4.2(a). 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 ∆R min = 0.05 0.1 0.2 0.4 0.6 pT(V) (GeV) R ( Z + 2J / γ + 2J ) 7 TeV (a) 0 100 200 300 400 500 600 700 800 1E-3 0.01 0.1 1 Z+2 jet, 7 TeV qqbar qg+gq gg qq pT(Z) (GeV) su bp ro ce ss fra ct io n (b) Figure 4.10.: (a) Ratio of the Z + 2 jets and γ + 2 jets pT (V ) distributions at 7 TeV, for different values of the ∆R(V, j) > ∆Rmin isolation cut. (b) Breakdown of the Z + 2 jet GAMBOS cross section into the different subprocess contributions defined in the text. Theoretical Studies 85 0 100 200 300 400 500 600 700 800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 7 TeV 1J 2J 3J pT(V) (GeV) R ( Z + n J / γ + n J ) (a) 1J P YT HI A ) γ Z/ / (R i P YT H IA ) γ Z/ (R 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 PYTHIA8 7 TeVi=2J i=3J (V) (GeV) T p 0 100 200 300 400 500 600 700 800 PY TH IA ) γ Z/ / (R G AM BO S ) γ Z/ (R 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 7 TeV1J 2J 3J (b) Figure 4.11.: (a) Z/γ + 1, 2, 3 jet GAMBOS cross section ratios as a function of pT (V ), with the isolation cut ∆Rmin = 0.4 . (b) Effect from multijet requirement on the PYTHIA8 ratio (upper) and difference with respect to GAMBOS (lower). For more than one jet, the additional jets in the PYTHIA8 simulation are produced by parton showering. In order to characterise the difference with respect to exact MEs, the following events were used for the 2– and 3–jet results from PYTHIA8 at the parton level, where the aim is to produce events with a similar parton level topology to the GAMBOS events based on the multijet MEs. In the 2–jet case, events were generated with both initial (ISR) and final state radiation (FSR) enabled and only those with exactly 2 jets within the allowed pT and y acceptance were considered. These jets either correspond to the parton from the hard scatter together with an ISR emission or from events with no accepted ISR emission, but where the hard parton, due to FSR, branches into two partons within the allowed acceptance. In addition, only events with the required V− jet and jet–jet ∆R separation were considered. The same event selection was used for the parton level 3–jet case, where the three jets either correspond to the hard parton together with two ISR emissions, or a FSR branch of the hard parton together with one ISR emission, or two FSR emissions. The multijet ratios from PYTHIA8 were found to be very similar to the one jet case. This is illustrated in the upper plot of figure 4.11(b), which shows the PYTHIA8 R2jet/R1jet and R3jet/R1jet ratios. 4 The corresponding GAMBOS Z/γ ratios 4The large deviation in the first bins is an artefact of the kinematic acceptance. In the 1–jet case, events will populate these bins according to the normal underlying distribution. However, since shower emissions can only occur with pT smaller than the hard process, the 2,3 jet events will be 86 Theoretical Studies are therefore slightly smaller as shown in the lower plot of figure 4.11(b). These results illustrate the difference between the two individual approaches in the multijet case as well as the importance of using a multiparton ME based program in the actual analysis, where the precision related to the ME calculation was discussed above in connection with figure 4.10. By comparing the GAMBOS and PYTHIA8 ratios at high pT , we can extract correction factors for the PYTHIA8 ratios to take account of the missing contributions, however, as seen in figure 4.11(b) these correction factors are not large. 4.4. Full event simulation The ability of PYTHIA8 to simulate full events was used both to investigate the robustness of the Z/γ cross section ratio as well as its potential use in estimating the Zνν background in searches for new physics at the LHC. For simplicity, the experimental aspects related to the photon analysis attempt to follow as closely as possible what is commonly used in ATLAS analyses [48,76], and for the new physics scenario we focus on the SUSY zero–lepton search [58,65], where SM Zνν production is one of the main backgrounds. Due to the phenomenological nature of this study, we neglect any experimental photon inefficiencies, apart from the isolation criteria discussed below, as well as any backgrounds (e.g. pi0 → 2γ), which in any case are expected to be relatively small in the high pT region of interest. 4.4.1. Effects on the ratio The same PYTHIA8 processes were used as in the parton–level study, but with the full parton shower, hadronisation, multiple interaction and particle decay simulation enabled. The default settings of v8.150 were used, for which general performance results can be found in [77]. The same selection was used as for the 1–jet parton–level results, here corresponding to an inclusive jet selection. The main differences with respect to the parton–level results come from using the final state boson momentum as well as from using jets reconstructed from the final state particles, rather than being represented by single partons. The jets were reconstructed using the FastJet library [52,78,79] and were based on all final–state particles except leptons and any photons with pγT > 30 GeV. The anti–kt algorithm was used with a R parameter of 0.4, also in accordance with the peaked toward the upper bin edge. Due to the sharp rise of the ratio at low pT , the average ratio value in these bins will therefore be significantly different for the higher jet multiplicities. Theoretical Studies 87 ATLAS analysis. In the following, these results from full event simulation are referred to as obtained at particle level. ) (GeV)γ( T p 0 100 200 300 400 500 600 700 800 (G eV ) T Is ol at io n E 0.5 1 1.5 2 2.5 PYTHIA8 7 TeV (a) (V) (GeV) T p 0 100 200 300 400 500 600 700 800 ) γ R (Z / 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (reco + iso)γZ/ (reco) γZ/ (part) γZ/ PYTHIA8 7 TeV (b) Figure 4.12.: (a) Transverse energy inside the photon isolation cone as a function of the photon pT . (b) Z/γ cross section ratio as a function of the photon pT . Parton (part) and particle level results (reco) are shown as well as for events passing the isolation criteria (reco + iso). The experimental analysis in ATLAS uses a photon isolation criterion in order to suppress QCD background and this quantity was found to be well described at MC generator level. This isolation criterion requires the transverse energy within a ∆R[= √ ∆η2 + ∆φ2] = 0.4 cone around the photon (EisoT ) not to exceed 4 GeV. Since the anticipated use of the ratio here is to estimate the number of Z events from measured γ events, the effect from this isolation requirement is also addressed. The fact that only isolated photons are considered implies an even stronger photon–jet separation than the one used above for the parton level results, ensuring an acceptance where GAMBOS provides robust calculations. The mean transverse energy within the photon isolation cone is shown in figure 4.12(a) as a function of the photon pT . This plot is based on events which pass the above selection applied to the final state photon as well as the reconstructed jets. A small increase with pT is shown, but with values well below 4 GeV over the whole range. In spite of the increasing hadronic recoil with larger boson pT , a relatively constant inefficiency of about 5% was found over the full pT range. 88 Theoretical Studies Figure 4.12(b) shows the Z/γ cross section ratio at parton (part) and particle level (reco) as well as at particle level where the isolation requirement is applied (reco+iso). Good agreement is evident between the results obtained at parton and particle level, where the difference is well below 5% at high pT , and the increase of the ratio due to the photon isolation criterion is of order 6% at high pT . 4.4.2. Background estimate for a 0` SUSY search (V) (GeV) T p 0 100 200 300 400 500 600 700 800 (pb /20 Ge V) T /d p σd -310 -210 -110 1 (no sel)γ (sel)γ Z PYTHIA8 7 TeV 2-jet (a) (V)η -3 -2 -1 0 1 2 3 (pb /0. 1) η /d σd -310 -210 -110 (no sel)γ (sel)γ Z PYTHIA8 7 TeV 2-jet (b) Figure 4.13.: (a) Boson pT and (b) η distributions from events passing the 2–jet SUSY selection. Results from photon events both with (sel) and without (no sel) applying the photon analysis selection are shown together with results from Z events (Z). This section demonstrates the estimation of Zνν background for a zero lepton SUSY search using photon events. This is done using the PYTHIA8 results and is meant to serve as a general example, since the method could be used also for other new physics searches where Zνν production contributes with a significant background. The method involves the following steps: • Photon event selection. Select a photon event sample using a loose enough selection, with respect to the photon and jets, to contain as many events as possible that will pass the final selection. This is represented here by the criteria pT (γ) > 45 GeV, |η(γ)| < 2.37, excluding 1.37 < |η(γ)| < 1.52 and EisoT < 4 GeV, based on the ATLAS photon analysis [48,76]. Theoretical Studies 89 (V) (GeV) T p 0 100 200 300 400 500 600 700 800 (pb /20 Ge V) T /d p σd -310 -210 -110 1 (no sel)γ (sel)γ Z PYTHIA8 7 TeV 3-jet (a) (V)η -3 -2 -1 0 1 2 3 (pb /0. 1) η /d σ d -310 -210 -110 (no sel)γ (sel)γ Z PYTHIA8 7 TeV 3-jet (b) Figure 4.14.: (a) Boson pT and (b) η distributions from events passing the 3–jet SUSY selection. Results from photon events both with (sel) and without (no sel) applying the photon analysis selection are shown together with results from Z events (Z). • SUSY event selection. Apply the SUSY selection to the photon events, where the photon pT represents the missing transverse energy from the Z in the events to be estimated. A 2–jet as well as 3–jet SUSY selection is used, based on the ATLAS search. 2–jet (3–jet): pT (j1) > 120 GeV, pT (j2) > 40 GeV, (pT (j3) > 40 GeV), |η(ji)| < 2.5, pT (V ) > 100 GeV, ∆φ(V, ji) > 0.4, pT (V )/meff > 0.3 and meff > 500 GeV. Here ji represents the i th leading jet and meff is the SUSY discriminating variable used in [58,65], defined as the scalar sum of the pT from the jets and the boson in the event. • Subtract backgrounds and correct for experimental efficiencies. This is represented here only by the isolation efficiency. • Convert photon events, inside the acceptance of the analysis, to Zνν events using the cross section ratio, R(pVT ) ·Br(Z → νν). As discussed in the previous sections, in an analysis of real LHC data, R(pVT ) should be based on results from exact multijet MEs and using an appropriate jet selection. • Correct for acceptance constraints implied by the photon analysis, e.g. the η(γ) selection criteria. 90 Theoretical Studies The main intention with this method is that all necessary corrections as well as theoretical input are related to the vector bosons, whereas all requirements with respect to the experimentally more challenging reconstructed jets, are identical for the Z and γ events. As shown in the previous section, the ratio is affected by requiring jets. However, since this effect is a consequence of changing the mixture of couplings imposed by the relevant initial partons together with their PDFs, it is small even for drastically different jet criteria and should be yet smaller with respect to experimental jet uncertainties, such as energy scale and resolution. The photon event selection imposes some unavoidable criteria which are not experi- enced by the Zνν background and therefore has to be corrected for. The implications of this selection on the final sample are, however, relatively mild for the following reasons. The photon pT requirement is significantly softer than the subsequent selection. A photon isolation criterion, of some kind, is required in order to obtain accurate calculations of the ratio. However, this is often also used in the SUSY selection for more experimental reasons, such as to prevent fake missing transverse energy caused by a high pT jet, i.e. the ∆φ(V, ji) requirement above. In addition, the fact that the Z and γ processes have the same phase space when pT MZ means that at high pT , the η distributions from the γ and Z events converge toward the same distribution, which becomes increasingly central with higher boson pT . Therefore any acceptance corrections will become the same for the Z as for the γ events. The SUSY selection, based on the pT of the boson and jets in the event, is then identical for the two event types and should not require any related corrections. Due to the fact that the bosons are recoiling against the hadrons, the SUSY selection will in principle act as a non–trivial high boson pT criteria. For this reason the γ events passing the SUSY selection can be converted into Z events based only on the boson kinematics. Again due to the convergence of the Z and γ phase space at high pT , the cross section ratio becomes insensitive to the particular η(V ) criteria used and is hence determined by the pT (V ). The precision of this method is therefore mainly related to the photon analysis part, which is expected to be precise at high photon pT , and the theoretical knowledge of the Z/γ cross section ratio. In figures 4.13 and 4.14 the boson pT and η distributions are shown after the 2–jet and 3–jet SUSY selections respectively. The distributions for photon events, with (sel) and without (no sel) passing the photon selection, as well as Z events (Z) are shown. The pT distributions show that both the SUSY selections mainly select events with a boson pT in the range 250 to 300 GeV. The η distributions also show the similarity in Theoretical Studies 91 shape of the distributions from the Z and γ processes. Both the pT and η distributions show that the effect from the photon selection, i.e. acceptance and isolation requirements, is relatively small also after the SUSY selection and the difference between the Z and γ results is consistent with the cross section ratio at relevant boson pT values. In the η distributions, the difference from applying the photon selection reflects the impact of the isolation criteria alone and it is shown that the additional jet requirements from the SUSY selections do not change the isolation efficiency dramatically. The results from the 2–jet and 3–jet selections do have slight differences, but the overall characteristics discussed are the same. Figure 4.15 shows the Z pT distributions from γ events passing the two SUSY selections, converted into Zνν according to the method outlined above, together with the results obtained from simulating Zνν directly. Since the PYTHIA8 ratios do not show any jet multiplicity dependence, the ratio shown in figure 4.12 (reco) was used in this analysis example for both the 2–jet and 3–jet results. As expected, the two distributions agree within the statistical uncertainty of the simulation, which is smaller than 5% in the bulk of the distributions. (Z) (GeV) T p 0 100 200 300 400 500 600 700 800 (pb /40 Ge V) T /d p σd -210 -110 1 γ from ννZ ννZ PYTHIA8 7 TeV 2-jet (Z) (GeV) T p 0 100 200 300 400 500 600 700 800 R at io 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 (a) (Z) (GeV) T p 0 100 200 300 400 500 600 700 800 (pb /40 Ge V) T /d p σd -210 -110 γ from ννZ ννZ PYTHIA8 7 TeV 3-jet (Z) (GeV) T p 0 100 200 300 400 500 600 700 800 R at io 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 (b) Figure 4.15.: Differential cross section as a function of pT (Z) for Z → νν events passing the (a) 2–jet and (b) 3–jet SUSY selection. The predictions using γ events (Zνν from γ) are compared to results from direct MC simulation of the Zνν process (Zνν). The uncertainties on the final background estimate, related to the experimental aspects of this analysis, are not covered by this study. However, as discussed above, the design of the method should limit the exposure mainly to the corrections from the 92 Theoretical Studies Selection RP ·Br RME ·Br εME εµ εPDF εTot 2–jet 0.254 0.234 5% 3% 4% 7% 3–jet 0.246 0.207 5% 3% 4% 7% Table 4.1.: The overall R ·Br values obtained after the SUSY selections, directly from PYTHIA8 (RP ) as well as corrected values with respect to the ME results (RME). The uncertainties associated with the ME calculation (εME), the scales (εµ) and the PDFs (εPDF ) are also shown. photon event selection, which are expected to be precise at high boson pT . In addition, as discussed in section 4.4.1, the impact associated with full event simulation on the cross section ratio was found to be small. As shown in figure 4.12(b), the ratio increases, by about 6% in the high pT region, when including the isolation efficiency, whereas a significantly smaller effect is seen when going from parton to particle level. The final uncertainties on R(Z/γ) from such effects are therefore expected to be at the percent level. A theoretical uncertainty, here with respect to the hard process calculations behind R(Z/γ) ·Br(Z → νν), that significantly exceeds 10% is therefore likely to dominate the uncertainty of the method. Table 4.1 presents the overall R ·Br values obtained for the results shown in figure 4.15. This includes both the value from PYTHIA8 (RP ), that was actually used in the plot, as well as the corrected value (RME) based on the ME results. The table also includes the uncertainties associated with the ME calculation (εME), the scales (εµ) and the PDFs (εPDF ), see section 4.3. The results show a total uncertainty of ±7% and indicate that the theoretical uncertainty for results obtained by an appropriately configured MC program, which uses ME amplitudes for the hard jets, should be within 10%. The SUSY selection used in the experimental analysis will evolve with an increasing amount of LHC data. However, such an evolution is expected to effectively imply a harder boson pT requirement and since the uncertainties in table 4.1 are valid for pT (V ) > 100 GeV, the same conclusions should hold also for harder selections.5 4.5. Summary One of the best methods to calibrate the irreducible background from Z(→ νν)+jets, to beyond the SM searches at the LHC, comes from using γ+jets data. The method 5At least up to pT (V ) = 800 GeV, which is the maximum value included in this study. Theoretical Studies 93 utilises the fact that at high boson pT (MZ) the event kinematics converge for the two processes and the cross sections differ mainly due to the boson couplings. The advantage comes from large statistics, compared to alternative methods using Z(→ ee, µµ)+jets events, together with the clean signature, with respect to experimental efficiencies and background, at high photon pT . Hence, a precise prediction from theory of the Z/γ cross section ratio, R(Z/γ), is required. The similarity between the two processes should allow for a robust prediction of R(Z/γ), given careful attention to the modelling of the jets. The general dependence of R(Z/γ) on the mixture of boson couplings, which is determined by the initial state partons of the relevant amplitudes and their corresponding PDFs, has been illustrated. Relatively accurate values can be obtained even using rough approximations in the 1–jet case, whereas a larger set of amplitudes becomes necessary when 2 or more jets are required. The ratios have been studied at parton level using both the (LO) PYTHIA8 as well as the (multijet ME) GAMBOS programs, which allows us to disentangle effects associated with the two approaches. The impact from exact MEs when requiring different numbers of jets was found to be significant, but uncertainties were found to be within 5% for the acceptance from typical experimental cuts. The corresponding uncertainties related to the PDFs and scale choice were found to be less than 4% and 3% respectively. The PYTHIA8 MC program was used to investigate effects on R(Z/γ) associated with full event simulation as well as performing a proof of principle analysis example. The effects investigated were found to be small and indicate that a theoretical precision6 at the 10% level is required, in order not to significantly degrade the performance of the method. The total theoretical uncertainty was found to be 7%, indicating that the results obtained by MC simulations, including exact multijet MEs, should be within the 10% level. These results should also hold for similar 2– and 3–jet selections, given that the effective pT requirement on the boson is harder than that used in the example analysis. Note that all our theoretical cross sections are evaluated in leading–order pQCD. It will be important to check, using for example the techniques of [64], that the ratio predictions are indeed stable – at least to the required accuracy – with respect to higher–order pQCD corrections. Finally, one type of correction that has not been included in our theoretical study is high-order electroweak corrections. Although these are intrinsically small, and many will again cancel in the Z/γ ratio, there is an important class of correction involving 6Again, referring to the hard QCD process calculations behind R ·Br. 94 Theoretical Studies W and Z virtual exchanges that does not cancel in the ratio. The impact on both the Z and γ distributions have been studied in [80,81]. It was shown that non-cancelling Sudakov-type logarithms ∼ α log2(pT (V )2/m2W ) appear at high pT (V ), and decrease the Z/γ + 1 jet ratio by 6% (11%) at pT (V ) = 300 (800) GeV [81]. However care is needed in the interpretation of this result, since the emission of real W bosons is expected to compensate the virtual Sudakov logarithms to some extent [82,83]. It is therefore important to carry out a full analysis of higher-order electroweak corrections for the multijet processes and acceptance cuts studied here. Chapter 5. Experimental Studies Given that plenty of advantages and theoretical results from the ZfromGamma method have been discussed in the previous two chapters, the remainder of this thesis focuses on presenting the main experimental work carried out to test it in ATLAS. This work was done in collaboration with S. Ask, T. J. Khoo and M. A. Parker from the University of Cambridge who were also members of the ATLAS Collaboration at the time of writing. The specific contributions from the author are specified at the end of this introduction. As mentioned, the ZfromGamma method has provided mainstream results for the SUSY 0` search since the beginning. In chronological order, results have been provided for the Moriond’11 [58], PLHC’11 [65], EPS’11 [54] and Moriond’12 [66] conferences. In this chapter, priority will be given to present the results for Moriond’12 as this is the latest analysis round, corresponding to the largest dataset (∼ 4.7fb−1). However, because of the evolution of this analysis since 2010 (see Section 3.4) and the multiple improvements carried out since, whenever possible brief comparisons will be given with respect to what was done in the previous analyses, and the more comprehensive versions are provided in Appendix C. Other supporting material is: Appendix A to show the plots from the Moriond’12 analysis which were not included in this chapter; Appendix B to summarise the relevant results from official prompt photon cross-section measurements in ATLAS, which are used to compare the results obtain here, e.g. Sections 5.3 and 5.5; and Appendix D to present the cross-checks done to validate the method. As for the next sections, the structure is the following: Section 5.1 briefly describes the software framework and provides all the relevant technical references. Section 5.2 details the event samples used from data and simulation. Section 5.3 describes the event selection to extract the inclusive prompt photon sample (γ + X). The rest of the method is presented in the same order as in the rightmost diagram of Figure 3.2 (for the case of 95 96 Experimental Studies Zνν background estimation): Section 5.4 outlines the subsequent selection made on the γ+X sample to define the Control Region sample (CR1a). The conversion of this control sample to Zνν events via a Transfer Function (TF) is detailed in Section 5.5. Finally, Section 5.6 explains the context and relevance of the results within the 0` analysis, as well as compares them to those from the alternative method which uses Z`` as calibrating sample (see Section 3.3). Supervised by S. Ask and M. A. Parker, the author performed most of the ZfromGamma- related work and plots for Moriond’11, PLHC’11 and EPS’11 found in Appendix C (see Appendix C for additional details), including the R&D that was required for the production of suitable MC samples. For Moriond’12 (presented in the following sections), the plots were done in collaboration with T. J. Khoo: the author provided the ZfromGamma algorithm and supervised the implementation of the method for this analysis round while T. J. Khoo took charge of migrating the ZfromGamma code to the ZeroLepton framework (see Section 5.1), as well as doing the necessary runs to process the Moriond’12 dataset. With respect to the 0` analysis, the author performed most of the work to obtain the CR1a-related results as specified above, except for most of the work presented in Section 5.6 which concerns their implementation into the 0` likelihood function, final background fitting and use for setting limits on SUSY models. However, Section 5.6.3 was also done in collaboration with T. J. Khoo. Similarly, all the results and plots showed from the other 0` CRs and SRs were done by other members from the 0` group in ATLAS. 5.1. Framework The main technical reference for this analysis can be found at [84], which provides the latest instructions to run the different steps of this analysis, as well as the links to the source code, software specifications and packages, names of samples used, etc. The framework has constantly evolved since its first implementation, Figure 5.1. The first version in 2010 [85] was an adaptation of the WZJratioAnalysis framework [86] – a C++ object-oriented ROOT-based package based on the TSelector class able to process data in D3PD (ntuple) format. The framework was then adapted to process SUSYD3PD’s. By 2011, the framework was significantly different from WZJratioAnalysis so a new name was given to it (ZfromGamma), however, the “tags” (versions) did not come into place until EPS’11 [87]. Experimental Studies 97 For the Moriond’12 0` analysis, ZfromGamma was migrated to the common ZeroLepton framework, which takes the object definitions from a common package to all ATLAS SUSY analyses (SUSYTools). This guarantees consistency between analysers, and with other SUSY analyses and ensures that up-to-date object definitions are used. The input histograms for the method are produced within the C++ code, while extraction of signal region estimates of the Z background is accomplished in post-processing, which is encapsulated within a python script. Details on the implementation are available on the twiki [88]. Analysis Framework Release SUSYD3PD tag Moriond’12 ZeroLepton-00-00-19 17 p832 EPS’11 ZfromGamma-00-00-01 16 p601/2 PLHC’11 ZfromGamma 16 p543 Moriond’11 WZJratioAnalysis 15 p305 Table 5.1.: Details of the frameworks used for the different analysis rounds since 2010, including the ATLAS software release and SUSYD3PD tag used. 5.2. Event Samples 5.2.1. Data The details of the data samples used for the different analyses rounds performed in 2011 are outlined in Table 5.2. As of writing, the Moriond’12 analysis was the most recent result, utilising the complete 2011 dataset, amounting to 4.7 fb−1 after application of some Data Quality (DQ) criteria – specifically, the 0` “Good Runs List” (GRL). In all cases, the data corresponds to a c.o.m. energy of √ s = 7 TeV and the Egamma stream. The data files are in SUSYD3PD format, made of AODs with the SUSYD3PDMaker package [89], with tags specified in Table 5.2. Data conditions varied throughout the 2011 run, with some of the most important dif- ferences highlighted in Table 5.2. Both machine (LHC) and detector (ATLAS) conditions changed in different data periods, with the detector conditions in particular mandating specific cuts that needed to be applied to the photon and 0` selections, amongst these: 98 Experimental Studies 1. “LAr Hole” – The loss of six front-end boards (FEBs) in the LAr calorimeter (ECAL, see Section 2.2.2) on April 30th made it impossible to read out cells in the second and third EM calorimeter layers in the region 0 < η < 1.4, −0.8 < φ < −0.6. These were partially recovered during the July technical stop, restoring measurement capability for the second layer. The loss meant that jets, electrons and photons falling into the hole could be partially or wholly unmeasured, introducing a major source of missing energy (see Appendix D.2). For PLHC’11, only data up to Period D was used, none of which was affected by this defect. However, the EPS’11 and Moriond’12 analyses had to introduce cuts to veto spurious missing energy events resulting from mismeasurement in the hole. At EPS’11, this was accomplished by a simple veto of any jets falling in the vicinity of the hole, while a more sophisticated check was used for Moriond’12, whereby for each jet the degree of mismeasurement and its contribution to the EmissT was taken into account. 2. “Dead Tile drawers” – Over the course of 2011, the proportion of non-functional Tile calorimeter (HCAL, see Section 2.2.2) cells rose from 0.2% to 5.1%. Such dead cells cause undermeasurement of jet energies, leading to fake EmissT . Prior to the Moriond’12 iteration, this problem was not considered. For Moriond’12, events with substantial EmissT arising from jets pointing to dead Tile drawers were vetoed. 3. “LAr errors” – Noise bursts and other defects in the LAr calorimeter can lead to the identification of false objects or their mismeasurement in other ways. Based on the shapes of the pulses read out from the LAr calorimeter and the status of the hardware, a flag is set that allows veto of events suffering from these issues. 4. “Bad jets” – A fraction of jets in data come from non-collision backgrounds such as beam halo and beam gas events, cosmic rays and calorimeter noise. The ATLAS Jet/Etmiss Combined Performance group provides a recipe for “Jet Cleaning”, and additional SUSY-group-specific cuts are used to eliminate events with identified bad jets. 5. “Bad EmissT ” – Due to compensation and noise in the calorimeter cells, occasional events may have a large number of cells measuring negative energies, producing substantial EmissT . Such events are vetoed. Event selection requirements based on the above are usually termed “event cleaning” cuts, e.g. cuts 3a-3i in Table 5.14. Experimental Studies 99 Analysis Dates Run Run number 〈µ〉 Peak L ∫ L dt SUSYD3PD period (1030cm−2s−1) (fb−1) tag 2011 data, √ s = 7 TeV Moriond’12 22/03-28/06 B2-M10 178044-191933 2.6-17.5 1.3-3600 4.710± 3.9% p832 EPS’11 22/03-30/10 B2-H4 178044-184169 2.6-7.97 1.3-1260 1.035± 4.5% p601/2 PLHC’11 22/03-29/04 B2-D7 178044-180481 2.6-7.0 1.3-660 0.165± 4.5% p543 2010 data, √ s = 7 TeV Moriond’11 30/03-29/10 A-I 152166-167844 1-3.5 1.3-210 0.035± 11% p832 Table 5.2.: Details of the data samples used for the different analyses; 〈µ〉 represents the peak mean number of interactions per bunch crossing. The integrated luminosity quoted is after the application of the SUSY GRL. Values taken from [13]. 5.2.2. Monte Carlo Monte Carlo simulated data samples are required not only to compare with data and assess the effectiveness of the method, but also to determine part of the Z/γ TF (Section 5.5). Therefore, samples are required for: (i)“prompt-photon + jets ”, (ii) backgrounds to “prompt-photon + jets ” and (iii) “Zνν + jets”. The goal of estimating the Zνν + jets background in EmissT + jets SRs drives the need for samples generated with large jet multiplicities. It is important to note that throughout the different analysis rounds, the availability of suitable MC samples evolved. In particular, substantial R&D studies had to be done to motivate the production of more suitable samples. The samples that were available in the previous analyses are listed in Appendix C. Some of these samples were superseded by more suitable ones and those currently in use are listed in Tables 5.3-5.6. Where possible, the same process is simulated with different generators in order to cross-check the results. A more detailed description of the process in (i), (ii) and (iii) above and their usage is now given. γ + jets These samples model the prompt photon signal with an inclusive number of jets. They are mainly used to determine part of the Z/γ TF (Equation (3.5)), such as RZ/γ, Aγ(pT) · εγ(pT), but also to calculate a few associated uncertainties and assess the impact from different generators. 100 Experimental Studies For Moriond’12, the two main generators used are ALPGEN and SHERPA, with the details given in Table 5.3. The SHERPA samples are produced in inclusive pT slices, with thresholds at 35, 70, 140, 280 and 500 GeV. “Enhancement factors” (intrinsic to the generator to deliberately generate a larger number of events in certain parts of phase space, which are assigned weights so that the correct cross section is obtained when used in the normalisation) are applied to boost statistics for events with 5 or 6 jets. Because the samples overlap, it is necessary to avoid double-counting by removing some of the MC events. This is done by dropping all events from the lower pT thresholds for which the hardest truth photon (mc status = 3, i.e. before showering) is above the next lowest pT threshold. Samples produced with ALPGEN come in two varieties: “standard” and “susyfilt”, where the former simply impose a 20 GeV photon pT threshold and the same for the additional partons in the matrix element. The susyfilt samples are similar, but have additional truth-level filter cuts that require the leading photon and jet to have pT > 100 GeV. These requirements improve the statistics for hard prompt photons, as required by this method. The standard and susyfilt samples also overlap, so any events in the standard samples with two truth jets above 100 GeV are vetoed (this is equivalent to vetoing events with a leading photon and a jet above 100 GeV). In addition to the configuration of the MC generator parameters, e.g. related to scales, PDFs, etc., the choice of the αem value is of particular interest for this process. To some extent counter-intuitively, as discussed for example in [64], the correct value assigned to the photon coupling in this process is believed to be the low energy value, αem(0) ∼ 1/137, instead of the running coupling value, αem(Q) ∼ 1/128, which is a consequence from selecting events with one real photon only (e.g. not including virtual contributions with photons decaying into lepton pairs). This is also what was used for the SHERPA samples and it is interesting to notice the good agreement with data obtained, straight from the MC predictions, in the following sections. Backgrounds to γ + jets When selecting prompt photon events in data, various background sources can contami- nate the selected sample. Hence, samples are required to evaluate the contribution from other SM processes to the photon selection at different stages of the analysis. A variety of samples using different generators are used, detailed in Table 5.5 and Table 5.6. Experimental Studies 101 The dominant low-pT background is from QCD events such as production of pi 0 → γγ. Additionally, electrons from W and top decays can be misidentified as photons. The electron contamination is also highly pT-dependent, due to the electron spectrum peaking around pT = mW/2 1, and is therefore expected to be small for a photon sample with pT > 100 GeV. Therefore, QCD multijet and W processes form the most important background samples. Zνν + jets These samples are mainly used for the computation of RZ/γ, but also for a direct comparison with the Zνν + jets estimate (from γ + jets). Again, multiple generators are used to evaluate the impact of theoretical variations. To be consistent with the γ + jets samples, ALPGEN and SHERPA are also used, with details given in Table 5.4. The SHERPA samples in this case are not pT-sliced, and include up to 5 jets in the matrix-element. Unfortunately, this hence results in a lack of statistics at high jet multiplicities, rendering the SHERPA MC unusable for many of the event selections in the 0` analysis. As for the ALPGEN samples, they are similarly divided into “standard” and “susyfilt” samples, and must have overlaps removed in a similar fashion. However, rather than filtering on two truth jets, in this case the leading truth jet and the truth EmissT are used instead. The MC statistics from ALPGEN are found to be adequate, and therefore ALPGEN samples are used for the computation of RZ/γ. Nevertheless, comparisons are made with SHERPA wherever possible. In the following pages, the SHERPA γ + jets will be shown only in the plots where a minimal selection for inclusive photon events has been applied, i.e. in all figures up to Figure 5.7. This is because of the filtering in the ALPGEN γ + jets samples already discussed, which misses a patch of phase space of events with a softer leading jet and photon. After imposing the 0` EmissT and leading jet cuts, the ALPGEN samples properly describe the data, and are used instead to be consistent with the Zνν + jets MC. 1Although applying jet requirements can have an effect on the lepton pT distribution, the background caused by these events remains negligible. 102 Experimental Studies Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 113714 SherpaY4JetsPt35 2.248 · 10+4 1.000 1.000 199999.0 113715 SherpaY4JetsPt70 1.774 · 10+3 1.000 1.000 198898.0 113716 SherpaY4JetsPt140 1.028 · 10+2 1.000 1.000 199899.0 113717 SherpaY4JetsPt280 3.997 · 10+0 1.000 1.000 199997.0 126371 SherpaY4JetsPt500 1.633 · 10−1 1.000 1.000 199993.0 106123 AlpgenJimmyGamNp1 7.411 · 10+4 1.000 1.000 100000.0 106124 AlpgenJimmyGamNp2 2.160 · 10+4 1.000 1.000 99998.0 106125 AlpgenJimmyGamNp3 5.801 · 10+3 1.000 1.000 99999.0 106126 AlpgenJimmyGamNp4 1.360 · 10+3 1.000 1.000 100000.0 106127 AlpgenJimmyGamNp5 3.522 · 10+2 1.000 1.000 99950.0 150090 AlpgenJimmyGamNp1 pt20 susyfilt 4.699 · 10+2 0.151 1.000 999893.0 150091 AlpgenJimmyGamNp2 pt20 susyfilt 4.571 · 10+2 0.170 1.000 1199697.0 150092 AlpgenJimmyGamNp3 pt20 susyfilt 2.309 · 10+2 0.222 1.000 1249891.0 150093 AlpgenJimmyGamNp4 pt20 susyfilt 8.427 · 10+1 0.289 1.000 749196.0 150094 AlpgenJimmyGamNp5 pt20 susyfilt 2.467 · 10+1 0.363 1.000 269995.0 150095 AlpgenJimmyGamNp6 pt20 susyfilt 7.260 · 10+0 0.457 1.000 74900.0 Table 5.3.: Moriond’12 Monte Carlo samples used to simulate the γ + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 118959 SherpaZ5jetstonunu30GeV 4.818 · 10+3 1.000 1.207 1699946.0 144069 SherpaZ5jetstonunu30GeV weighted 5.155 · 10+3 1.000 1.128 984999.0 107710 AlpgenJimmyZnunuNp0 pt20 filt1jet 3.572 · 10+3 0.011 1.260 54949.0 107711 AlpgenJimmyZnunuNp1 pt20 filt1jet 7.387 · 10+2 0.611 1.260 909848.0 107712 AlpgenJimmyZnunuNp2 pt20 filt1jet 2.229 · 10+2 0.882 1.260 169899.0 107713 AlpgenJimmyZnunuNp3 pt20 filt1jet 6.187 · 10+1 0.968 1.260 144999.0 107714 AlpgenJimmyZnunuNp4 pt20 filt1jet 1.563 · 10+1 0.992 1.260 309899.0 144017 AlpgenJimmyZnunuNp5 excl pt20 filt1jet 3.581 · 10+0 0.998 1.260 185000.0 144021 AlpgenJimmyZnunuNp6 pt20 filt1jet 9.220 · 10−1 1.000 1.260 114999.0 144192 AlpgenJimmyZnunuNp1 pt20 susyfilt 3.683 · 10+1 0.349 1.260 499898.0 144193 AlpgenJimmyZnunuNp2 pt20 susyfilt 3.429 · 10+1 0.296 1.260 399999.0 144194 AlpgenJimmyZnunuNp3 pt20 susyfilt 1.612 · 10+1 0.335 1.260 299998.0 144195 AlpgenJimmyZnunuNp4 pt20 susyfilt 5.481 · 10+0 0.397 1.260 184998.0 118962 AlpgenJimmyZnunubbNp0 pt20 filt1jet 3.280 · 10+1 1.000 1.260 604499.0 118963 AlpgenJimmyZnunubbNp1 pt20 filt1jet 1.450 · 10+1 1.000 1.260 280999.0 118964 AlpgenJimmyZnunubbNp2 pt20 filt1jet 5.240 · 10+0 1.000 1.260 102000.0 118965 AlpgenJimmyZnunubbNp3 pt20 filt1jet 1.560 · 10+0 1.000 1.260 30500.0 Table 5.4.: Moriond’12 Monte Carlo samples used to simulate the Zνν + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Experimental Studies 103 Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 105890 AlpgenJimmyttbarlnlnNp0 3.466 · 10+0 1.000 1.690 117999.0 105891 AlpgenJimmyttbarlnlnNp1 3.399 · 10+0 1.000 1.690 159999.0 105892 AlpgenJimmyttbarlnlnNp2 2.124 · 10+0 1.000 1.690 336897.0 117897 AlpgenJimmyttbarlnlnNp3 baseline 9.470 · 10−1 1.000 1.690 148000.0 117898 AlpgenJimmyttbarlnlnNp4 baseline 3.341 · 10−1 1.000 1.690 60000.0 117899 AlpgenJimmyttbarlnlnNp5 baseline 1.275 · 10−1 1.000 1.690 7000.0 105894 AlpgenJimmyttbarlnqqNp0 1.376 · 10+1 1.000 1.770 647396.0 105895 AlpgenJimmyttbarlnqqNp1 1.361 · 10+1 1.000 1.770 652997.0 105896 AlpgenJimmyttbarlnqqNp2 8.418 · 10+0 1.000 1.770 146999.0 117887 AlpgenJimmyttbarlnqqNp3 baseline 3.776 · 10+0 1.000 1.770 652495.0 117888 AlpgenJimmyttbarlnqqNp4 baseline 1.336 · 10+0 1.000 1.770 118999.0 117889 AlpgenJimmyttbarlnqqNp5 baseline 5.040 · 10−1 1.000 1.770 8000.0 117360 st tchan enu AcerMC 6.970 · 10+0 1.000 1.000 999295.0 117361 st tchan munu AcerMC 6.970 · 10+0 1.000 1.000 999948.0 117362 st tchan taunu AcerMC 6.970 · 10+0 1.000 1.000 998995.0 117363 st schan enu AcerMC 5.000 · 10−1 1.000 1.000 199899.0 117364 st schan munu AcerMC 5.000 · 10−1 1.000 1.000 199850.0 117365 st schan taunu AcerMC 5.000 · 10−1 1.000 1.000 200000.0 105500 AcerMC Wt 1.574 · 10+1 1.000 1.000 994897.0 119353 PythiaMadgraph ttbarW 1.244 · 10−1 1.000 1.300 100000.0 119354 PythiaMadgraph ttbarWj 8.347 · 10−2 1.000 1.300 100000.0 119355 PythiaMadgraph ttbarZ 9.558 · 10−2 1.000 1.300 99997.0 119356 PythiaMadgraph ttbarZj 8.160 · 10−2 1.000 1.300 100000.0 119583 PythiaMadgraph ttbarWW 1.249 · 10−3 1.000 1.300 100000.0 Table 5.5.: Moriond’12 Monte Carlo samples used to simulate the SM background to the γ+ jets signal from top quark production, including cross section times filter efficiency, k-factor and the number of generated events in the sample. 104 Experimental Studies Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 107680 AlpgenJimmyWenuNp0 6.932 · 10+3 1.000 1.196 3458883.0 107681 AlpgenJimmyWenuNp1 1.305 · 10+3 1.000 1.196 2499645.0 107682 AlpgenJimmyWenuNp2 3.780 · 10+2 1.000 1.196 3768632.0 107683 AlpgenJimmyWenuNp3 1.019 · 10+2 1.000 1.196 1008947.0 107684 AlpgenJimmyWenuNp4 2.570 · 10+1 1.000 1.196 250000.0 144018 AlpgenJimmyWenuNp5 excl pt20 5.814 · 10+0 1.000 1.196 979197.0 144022 AlpgenJimmyWenuNp6 pt20 1.546 · 10+0 1.000 1.196 144998.0 144196 AlpgenJimmyWenuNp1 pt20 susyfilt 1.305 · 10+3 0.006 1.196 180899.0 144197 AlpgenJimmyWenuNp2 pt20 susyfilt 3.780 · 10+2 0.017 1.196 134998.0 144198 AlpgenJimmyWenuNp3 pt20 susyfilt 1.019 · 10+2 0.034 1.196 139999.0 144199 AlpgenJimmyWenuNp4 pt20 susyfilt 2.570 · 10+1 0.056 1.196 75000.0 107650 ZeeNp0 6.696 · 10+2 1.000 1.243 6618284.0 107651 ZeeNp1 1.346 · 10+2 1.000 1.243 1334897.0 107652 ZeeNp2 4.065 · 10+1 1.000 1.243 2004195.0 107653 ZeeNp3 1.126 · 10+1 1.000 1.243 549949.0 107654 ZeeNp4 2.840 · 10+0 1.000 1.243 149948.0 107655 ZeeNp5 7.600 · 10−1 1.000 1.243 50000.0 109300 AlpgenJimmyZeebbNp0 nofilter 6.570 · 10+0 1.000 1.243 409999.0 109301 AlpgenJimmyZeebbNp1 nofilter 2.480 · 10+0 1.000 1.243 160000.0 109302 AlpgenJimmyZeebbNp2 nofilter 8.900 · 10−1 1.000 1.243 60000.0 109303 AlpgenJimmyZeebbNp3 nofilter 3.900 · 10−1 1.000 1.243 30000.0 116250 AlpgenJimmyZeeNp0 Mll10to40 pt20 3.055 · 10+3 1.000 1.243 994949.0 116251 AlpgenJimmyZeeNp1 Mll10to40 pt20 8.491 · 10+1 1.000 1.243 299998.0 116252 AlpgenJimmyZeeNp2 Mll10to40 pt20 4.119 · 10+1 1.000 1.243 999946.0 116253 AlpgenJimmyZeeNp3 Mll10to40 pt20 8.350 · 10+0 1.000 1.243 149998.0 116254 AlpgenJimmyZeeNp4 Mll10to40 pt20 1.850 · 10+0 1.000 1.243 40000.0 116255 AlpgenJimmyZeeNp5 Mll10to40 pt20 4.600 · 10−1 1.000 1.243 10000.0 126013 Sherpa Wenugamma 1jet 7.287 · 10+1 1.000 1.000 399899.0 126014 Sherpa Wmunugamma 1jet 7.287 · 10+1 1.000 1.000 399948.0 126017 Sherpa Znunugamma 1.035 · 10+0 1.000 1.000 100000.0 126018 Sherpa Wenugamma highpt 2.966 · 10+0 1.000 1.000 299947.0 126019 Sherpa Wmunugamma highpt 2.964 · 10+0 1.000 1.000 299999.0 126022 Sherpa Znunugamma highpt 2.316 · 10+0 1.000 1.000 200000.0 117410 AlpgenJimmyWgammaNp0 pt20 2.133 · 10+2 1.000 1.000 1459648.0 117411 AlpgenJimmyWgammaNp1 pt20 5.223 · 10+1 1.000 1.000 529998.0 117412 AlpgenJimmyWgammaNp2 pt20 1.726 · 10+1 1.000 1.000 175000.0 117413 AlpgenJimmyWgammaNp3 pt20 5.334 · 10+0 1.000 1.000 264999.0 117414 AlpgenJimmyWgammaNp4 pt20 1.376 · 10+0 1.000 1.000 64999.0 117415 AlpgenJimmyWgammaNp5 pt20 3.444 · 10−1 1.000 1.000 20000.0 Table 5.6.: Moriond’12 Monte Carlo samples used to simulate the SM background to the γ+ jets signal from vector boson production, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Experimental Studies 105 Modelling data conditions Note that each of the listed samples is generally available in more than one software production, depending on the analysis round for which it was used, to reflect the different data-taking conditions discussed in Sections 2.2.4, 5.2.1 and Table 5.2. Some of the MC production details are given in Table 5.7. For example, for Moriond’12, the productions were “mc11b” and “mc11c”, which were designed to be compatible with 2011 ATLAS data by applying specific MC event generator and detector simulation settings (more details can be found in [90,91]). A more refined simulation of the different pileup conditions is done “offline” (at analysis-level) using the ATLAS default pileup reweighting tool. This tool calculates an event weight for MC events, based on a given data sample, since when the MC samples are first produced, only a “best-guess” of the data pileup conditions can be made. For PLHC’11 and EPS’11, the introduction of this tool resulted in a MC inefficiency of ∼ 50% (see Section C.2.2). Additionally, some detector conditions such as the LAr hole were not reflected in the MC as the simulation conditions were prepared well in advance of data taking. For Moriond’12, the data-taking conditions for the entire dataset were already known. Hence it was possible to account for all important detector conditions e.g. the LAr hole and dead tile drawers, as well as to simulate better the pile-up conditions in the corresponding MC productions. Analysis Production Release 〈µ〉 Moriond’12 mc11b/c 17 6.3-11.6 EPS’11 mc10b 16 8 PLHC’11 mc10a 16 8 Moriond’11 mc09 15 1-3.5 Table 5.7.: Details of the MC production used for the different analyses, including MC production and mean number of interactions per event 〈µ〉. In all cases, the c.o.m. is √s = 7 TeV and GEANT4 is used for ATLAS detector simulation. The main difference between mc11b and mc11c is the PYTHIA tune used to generate the pileup events. In all the plots that follow, unless otherwise stated, whenever MC is shown, the normalisation is to the data luminosity and using the cross-sections listed in this section. 106 Experimental Studies 5.3. Inclusive Photon Sample (γ +X) As mentioned in Section 3.4, for each 0` SR, a photon event sample suitable for estimating the Z boson background is selected in two stages. These two stages are defined so that after the first stage: (i) the resulting sample is common to all SRs; (ii) the selection matches that from the ATLAS prompt photon cross section analysis , e.g. [48, 49,92]; and (iii) a first cross-check can therefore be made with these official results, e.g. the efficiency and purity should be the same given the identical event selections. This Section describes the first stage, referred to in this thesis as the inclusive photon selection (γ +X). 5.3.1. Object definitions The photon object definitions implemented here are identical to the latest used by the ATLAS Standard Model Direct Photon (SMDP) group [93] (based on the ATLASegamma group recommendations [94–96]) as follows: Preselected photons: Defined as reconstructed photons (see Section 2.2.5) which pass the following criteria in Table 5.8: • Energy Scale - The appropriate electromagnetic energy scale is extracted by using electrons from Z boson decays and the well-known Z-mass shape. The corresponding corrections are applied on the energy of all data candidates using the EnergyRescaler tool provided by the egamma group [97]. Since the MC does not perfectly reproduce the energy resolution in data, a smearing procedure is also applied to all MC candidates. • Object Quality - Candidates must satisfy the egamma Object Quality selec- tion [94]. • Photon Cleaning - Candidates must pass the egamma prescription, based on the LAr cell quality factor and timing (related to selections on some shower shape variables [94]). This removes fake photons associated to noise bursts in the LAr calorimeter. • Photon Quality - Candidates must pass the SMDP tight isEM cuts, recomputed with the PhotonIDTool [93] after having applied the EnergyRescaler on all relevant discriminating variables. Experimental Studies 107 • η Acceptance2 - Photons are required to be away from the ECAL barrel/endcap transition region (1.37 ≤ |η| < 1.52) and within the acceptance of the high granularity regions (|η| < 2.5, see Table 2.4). Signal photons: Defined as preselected photons as above, which in addition pass the following criteria in Table 5.8: • Identification (ID) - To discriminate the prompt photon signal from the back- ground, cuts are applied on a series of electromagnetic shower shape variables, based on the lateral and longitudinal energy profile of the shower in the ECAL. For all analyses, the “RobustTight” identification criterion (referred to here as “tight”) was used and the its precise definition can be found in [48]. Overall, this criterion does not depend on the photon pT, but on its η (to take into account variations in the calorimeter geometry and material). • Isolation - To further discriminate signal from background, an isolation re- quirement is made on the remaining photon candidates after preselection and identification. This is because the prompt photon signal is expected to be more isolated with respect to hadronic activity than the background, as shown in Figure 5.13. The isolation variable EisoT is computed from the transverse energy deposited in the calorimeters in a cone of radius ∆R = 0.4 around the photon candidate. A few corrections are made to EisoT to account for the effects associated with the energy of the photon candidate itself, the underlying event and pileup (see Section 2.2.5). The overall correction from these was found to be ∼ 900 MeV [49], after which EisoT is directly comparable to parton-level theoretical predictions (e.g. an experimental EisoT < 3 GeV cut is similar to applying a theoretical 4 GeV cut). Prompt photon (γ1): Defined here as the leading-pT signal photon in an event. These are the candidates considered further when resolving overlapping objects, such as jets (see Section 5.4). As appreciated from Table 5.8, the object definitions have evolved throughout the different analysis rounds to deal with different data-taking conditions (see Section 5.2.1) and improve photon measurements (ID, efficiency, etc). 2The photon η used here is the one computed in the second sampling of the LAr calorimeter, which is denoted as ηs2 in [49] but here referred to simply as η. 3At the time, this variable was known to not be perfectly modelled by the MC, hence the lack of a perfect data/MC agreement in the figures. 108 Experimental Studies Reconstructed Photon Definitions Cut Specification Moriond’12 EPS’11 PLHC’11 Moriond’11 Preselected γ Energy Scale ” ” ” rescaling (data) / smearing (MC) Object Quality ” ” OQ flag OQ check (data) / OQ map (MC) Cleaning ” OQ, LAr quality jet cleaning none & timing η Acceptance ” ” |ηs2| < 2.37 |ηs2| < 1.81 ” ” & not in crack Signal γ Identification ” ” ” RobustTight Isolation Etcone40 < 5 GeV ” ” Etcone40 < 3 GeV Table 5.8.: Summary of the selection criteria for the different photon definitions used (the ” means the definition didn’t change with respect to to the previous analysis). The leading pT signal photon in an event defines the prompt photon candidate. The “crack” region and ηs2 are defined elsewhere in the text and “OQ” stands for Object Quality. -5 0 5 10 15 20 25 30 351 10 210 310 410 510 610 710 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD RT_ph_Etcone40_corrected [GeV] En tri es /1 .0 G eV En tri es /1 .0 G eV En tri es /1 .0 G eV En tri es /1 .0 G eV En tri es /1 .0 G eV En tri es /1 .0 G eV (a) ph_Etcone40_corrected [GeV] -10 0 10 20 30 40 50 Ev en ts / 5 0 G eV 10 210 310 410 510 610 710 810 910 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Sherpa)γV + jets (Sherpa)γ QCD multijets InternalATLAS CR1a SRA ph_Etcone40_corrected [GeV] -10 0 10 20 30 40 50 DA TA / M C 0 0.5 1 1.5 2 2.5 (b) Figure 5.1.: Isolation variable EisoT distribution for preselected “tight” photon candidates in data and MC. The MC include γ+ jets signal and backgrounds to γ+ jets, (a) in the Moriond’11 dataset (showing QCD background only) and (b) in the Moriond’12 dataset (showing both QCD and electroweak backgrounds). The width of the EisoT spectrum for the signal is driven by noise in the EM calorimeter, which is calibrated to be centred at zero, hence the negative component corresponding to downward fluctuations in the calorimeter cells. Experimental Studies 109 5.3.2. Event Selection The event selection performed in this first stage of the analysis is outlined in Table 5.9. Cut 1 is to ensure the same data-quality (DQ) requirements as in the 0` analysis. Events are required to be in the same Good Runs List (GRL), which also determines the total integrated luminosity of the sample, quoted in Table 5.2. With the exception of Cut 1, the event selection is also identical to the latest used by the SMDP group [93]. Cut 2 is the trigger decision, always chosen to be the lowest unprescaled photon trigger in the dataset. Cut 3-4 are general “event cleaning” cuts applied widely in ATLAS analyses. Cut 3 in particular rejects events with bad data quality in the LAr calorimeter [94] (see Section 5.2.1). Cut 4 ensures that the event is a genuine collision event with a well-defined interaction at the primary vertex (PV)4, as opposed to being from non-collision sources such as cosmic rays. Lastly, Cut 5 ensures the photon candidates are in the ∼ 100% efficient trigger plateau from Cut 2. γ +X Event Selection Cut Description Specification Moriond’12 EPS’11 PLHC’11 Moriond’11 1 0` GRL (data) x-v36-prod10y-08z x-v*-prod*y-0*z x-v*-prod*y-0*z N/A 2 Trigger ” g80 loose g60 loose g40 loose 3 Ev. clean - LAr (data) ” larError=0 none none 4 Ev. clean - leading PV ” Ntrk ≥ 5 ” Ntrk ≥ 3 5 pT(γ1) ” > 85 GeV > 65 GeV > 45 GeV Table 5.9.: Event selection defining the inclusive prompt photon sample (γ+X) in the different analysis rounds. In Cut 1, x=data11 7TeV.periodAllYear DetStatus-; y= CoolRunQuery-00-04-; and z= Susy.xml. For the trigger names in Cut 2, “g” is for “gamma”, the number represents the transverse energy threshold and “loose” the type of ID requirement. Cut 3 checks the LAr DQ flag is not in ERROR (noise burst) or WARNING (noisy) state. In Cut 4, Ntrk is the number of associated tracks to the PV. In Cut 5, γ1 represents the prompt photon candidate as defined in Section 5.3.1. 5.3.3. Results Table 5.10 shows the number of photon candidates passing the object definitions in Ta- ble 5.8, for events that pass the selection in Table 5.9. Only those events with at least 4The leading primary vertex is defined as the vertex with the highest ∑ |pT|2 of tracks. 110 Experimental Studies one signal photon candidate are kept and these define the “γ+X sample”. Although it is possible for an event to have more than one signal photon, e.g. a diphoton event γγ + Y , only the highest-pT photon is considered as the prompt photon candidate, and so the total number of candidates equals the total number of events. Figure 5.2 shows the pT and η distributions of the prompt photon candidates in the γ +X sample. As expected (see Appendix B), the background reduces with photon pT, shown by the increasing agreement of data with the MC signal. The average jet multiplicity in these events is suggested by the recent SMDP γ + jets cross-section measurement results [98], where on average it is found to be between 1.3 and 2.0, and increasing with photon pT. Number of γ candidates Requirement Moriond’12 EPS’11 PLHC’11 Moriond’11 Preselection 11 951 974 - - 722 055 Identification 3 926 910 - - 255 985 Isolation 2 858 432 523 745 230 457 152 602 Table 5.10.: Cutflow of reconstructed photons in data which passed the event selection in Table 5.9 under different object definitions in Table 5.8 for the different analyses. Only those passing up to the isolation requirement are considered part of the γ +X sample. It is possible to have events with more than one signal photon ( e.g. in the PLHC’11 dataset, 71 events are diphoton events) but for the purposes of this analysis, only the leading pT one is considered the prompt photon. The ‘-’ means the information was not available at the time of writing. [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 310 410 510 610 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (a) [GeV] T Photon p -3 -2 -1 0 1 2 3 Ev en ts / 50 G eV 10 210 310 410 510 610 710 810 910 1010 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A [GeV] T Photon p -3 -2 -1 0 1 2 3 D AT A / M C 0 0.5 1 1.5 2 2.5 (b) Figure 5.2.: Moriond’12 leading-pT photon (prompt photon candidate) (a) pT and (b) η distributions from data and MC after the γ +X selection. The number of events in these plots is quoted in Table 5.10. Experimental Studies 111 5.3.4. Comparison with SM prompt photon results The event sample obtained after the inclusive photon selection (γ + X) was used for cross checks with respect to official results from ATLAS prompt photon cross-section measurements. These comparisons serve both to validate the selection procedure as well as to provide reference results before the final selection is applied. The final selection (Section 5.4), motivated by the new physics search and specific to this analysis, is expected to only have small effects on several properties of the photon event sample, particularly those related to efficiencies and backgrounds. It is therefore very valuable to establish a reference before the final selection, which can confirm this expectation and be verified by other independent analysis results. Two measurements of the prompt photon cross-section have been made in ATLAS: one in 2010 with 880 nb−1 [48] and an update of it in 2011 with 35 pb−1 [49]. A summary of the 35 pb−1 analysis (referred to here as the “SM analysis”) is provided in Appendix B, as this is the main reference used in this analysis. However, more recent updates exist (albeit unpublished), such as [92] (1.08 fb−1). To ease comparison with the 35 pb−1 analysis results, the rest of this section will present the Moriond’11 results (Appendix C.1), since this is the analysis round which corresponds to roughly the same luminosity. Despite the results being relatively old, the main conclusions also hold for the more recent updates. As seen in Sections 5.3.1-5.3.2, the event selection and object definitions have changed little since then, so in practice, the main change simply comes down to an increase in luminosity. Acceptance and Efficiency (Aγ · εγ) - The acceptance Aγ derives from the limited fiducial region in which photons can be properly reconstructed in ATLAS (η re- quirements in Table 5.8). Given that the same photon pT and η acceptance as in [49] are used, no additional acceptance corrections are necessary. As discussed in Appendix B, the efficiency at this stage refers to the overall photon efficiency of reconstruction and identification, i.e. εγ = εγrec · εγid. Usually the isolation criterion is not taken into account in the efficiency of the photon results in [49], but instead included in the theoretical predictions with which they are compared. Therefore, here an additional efficiency εγiso is defined with respect to the isolation requirement. This is, however, closely related to the Control Region selection (Section 5.4) and becomes only relevant when calculating the TF, therefore its discussion is left until Section 5.5.1. 112 Experimental Studies The reconstruction inefficiency (1− εγrec) is caused by limitations of the reconstruc- tion algorithm, acceptance loss due to dead calorimeter cells and object quality requirements. In[48,49], εγrec was estimated from prompt photon MC as a function of η and pT, and found to be relatively constant within the relevant photon acceptance, slightly decreasing with larger pT and with some variation in η (see Figure B.2). The dominant source of the identification inefficiency (1− εγid) is the tight photon identification requirement. Here as well, εγid was estimated in [48,49] from prompt photon MC and found to be relatively constant within the relevant photon acceptance, but unlike εγrec, ε γ id increased with pT (see Figure B.3). As a cross check, the shower shape variables, plots of which are shown in Figure C.3, were investigated in data and MC and found to be consistent with the SM analysis results. These variables were also compared before and after the final Moriond’11 0` selection (see Section 5.4) and found not to change significantly, even suggesting a higher efficiency after the final selection, as expected due to the higher photon pT in the final sample (see Section 5.4.3). Overall, the relatively stable behaviour of the efficiency, especially at high pho- ton pT, indicates that the efficiency estimated in the SM analysis should also be representative after the final selection in this analysis, as long as the resulting pT and η distributions are folded in. This, together with the high precision expected from estimating these efficiencies using MC, as done in this analysis, should allow for a relatively precise comparison between the final efficiency estimate and the SM analysis results. Purity (P ) - As shown in the SM analysis, the expected purity (1− fbkg) is very high when requiring a high photon pT (∼ 99%, see Table B.3) . This is mainly due to the isolation criterion, which becomes more efficient at high pT because harder jets tend to be more collimated and it is less likely for a pi0 to remain isolated. This is in contrast to the tight identification requirement, which can more efficiently reject background at lower pT (e.g. the rejection power is better for softer pi 0, because the first layer of the LAr calorimeter can more easily resolve the two photons produced in the pi0 decay). Figure 5.1 shows the isolation energy (EisoT ) distribution for the Moriond’11 and Moriond’12 samples of preselected tight photon candidates. It indicates the concen- tration of QCD background in the tail region at large EisoT values. The results also demonstrate a slight disagreement between data and MC for this variable, which is Experimental Studies 113 characterised by data being shifted toward larger values by ∼ 2 GeV (this will be discussed further in Section 5.5.1 in connection to the isolation efficiency). Similar distributions for different photon pT ranges are shown in Figure B.5 to illustrate how the QCD background propagates to larger EisoT values as the photon pT increases. At high photon pT, the remaining background consists primarily of electrons, e.g. from Weν decays, faking a photon. However, this background is also at the 1% level for photon pT requirements which are significantly above mW/2 [99]. Figure 5.3 shows the photon pT distribution of candidates passing the object definitions in Table 5.8, for events that pass the selection in Table 5.9. Figure 5.3(a) corresponds to preselected photons, where the sample can be seen to be still highly contaminated by QCD background (a purity of about 20%) in an approximately even distribution over the whole pT range. Figure 5.3(b), on the other hand, shows the same distribution after the full prompt photon selection, i.e. including the tight identification and the photon isolation requirements. Despite the LO precision of the PYTHIA MC, the overall trend is consistent with the results found in the SM analysis, where for pT(γ1) > 100 GeV the purity exceeds 90%, and the background becomes negligible at pT(γ1) ∼ 200 GeV. 0 100 200 300 400 500 600 700 800 1 10 210 310 410 510 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD PS_ph_cl_et [GeV] En tri es /2 0. 0 G eV En tri es /2 0. 0 G eV (a) 0 100 200 300 400 500 600 1 10 210 310 410 -1L dt ~32 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_pt [GeV] En tri es /1 0. 0 G eV En tri es /1 0. 0 G eV IRT_ph_pt [GeV]0 100 200 300 400 500 600 D AT A/ M C sig na l 0 0.5 1 1.5 2 2.5 (b) Figure 5.3.: Moriond’11 pT distribution of photon candidates passing the (a) preselection and (b) prompt photon definitions in Table 5.8. The MC shown is the γ + jets signal and QCD background from PYTHIA (see Appendix C.1.2). Signal yield (Nγ) - The signal yield results obtained were also found consistent with those in [49]. As an example, in the Moriond’11 dataset the number of observed prompt photon candidates NobsA in the (|η|, pT) range ([0.60; 1.37), [45; 55) GeV) was 32 272. In this (|η|, pT) bin, the expected purity is ∼ 90%. For the same |η| range 114 Experimental Studies but higher pT range [200; 400) GeV, the expected purity is ∼ 100% and NobsA was 185. These numbers can be compared with the SM analysis equivalent quoted in Table B.3. A small difference is expected from the different GRLs used and the slightly higher luminosity in the Moriond’11 dataset (see Section B.1). Experimental Studies 115 5.4. Control Region Sample (CR1a) The steps shown in Figure 3.2 required to go from the “γ +X events” to the “CR events” are of course a simplified version – in practice a few more steps are required as shown in Figure 5.4, which consist of additional object definitions and event selections (on top of those defining the γ + X sample). The details of these requirements are described in this Section, but beforehand it is helpful to define more precisely the following concepts which are constantly used in the following pages: Signal Region (SR) - Defined by an event selection optimised for discovery, i.e. with sufficient sensitivity to a BSM model. In the case of the SUSY 0` analysis, the aim is to maximise sensitivity to the production of heavy SUSY particles decaying into jets and neutralinos, leading to final-states of EmissT + jets. In the various 0` analyses, several SRs are defined, typically differentiated by jet multiplicity and thresholds on the discriminating variables, e.g. meff cut, defined below. Control Region (CR) - Defined by an event selection as similar as possible to the SR (to minimise the uncertainties arising from extrapolation to the SR while maintaining an adequate statistical weight) and enriched in the chosen calibrating process, i.e. of high-purity. Measurements in a CR are used to estimate a particular background in the SR via the TF (Section 5.5). Example of CRs in the 0` analysis are shown in Table 5.11 and the detailed definitions are discussed until Section 5.6. CR1a - This is the Control Region based on the γ + jets sample, used to estimate the Zνν + jets background in the 0` analysis. More specifically, it is the γ + X event sample, as defined in Section 5.3, which also passes the additional requirements described in Sections 5.4.1 and 5.4.2 (see Figure 5.4). CR1b - This is the alternative CR to CR1a based on a Z`` + jets sample as outlined in Table 5.11. Channel - This term is used to refer to the ensemble of a SR and its corresponding CRs, e.g. for Moriond’12, six channels are defined, where each SR has five associated CRs. 116 Experimental Studies CR SR Background CR process CR selection CR1a Zνν + jets γ+jets Isolated photon CR1b Zνν + jets Z`` + jets |m(`, `)−m(Z)| < 25 GeV CR2 QCD jets QCD jets Reversed ∆φ cut CR3 W`ν + jets W`ν + jets 30 GeV < mT (`, E miss T ) < 100 GeV, b-veto CR4 tt¯ and single-t tt¯→ bbqq′`ν 30 GeV < mT (`, EmissT ) < 100 GeV, b-tag Table 5.11.: Control Regions used in the 0` analysis, indicating the main SR background targeted, the process used to calibrate the background, and main CR cuts used to select this process. The meaning of the selections and variables can be found in Section 5.6 and [100]. 5.4.1. CR1a Object Definitions As indicated in Figure 5.4, these additional requirements are conjunctively referred to as ‘CR1a Object Definition’ because within the context of the 0` analysis they only apply to CR1a, i.e. in the rest of the 0` analysis, prompt photon events are ignored5. The CR1a object definition then consists of the following: i. γ1-jet Overlap Removal: Experimentally, this step is required when the jets in photon events need to be defined. This is because in ATLAS photons are also reconstructed as jets, as suggested by Figure 5.5. So, to prevent the reconstructed photon from being double-counted as a jet, a γ1-jet overlap removal procedure is required. The recipe used here is to remove any jets with ∆R < 0.2 of the prompt photon candidate γ1. It was found that varying the critical ∆R value between 0.1 and 0.4 introduces negligible bias, as is to be expected given the prior application of photon isolation criteria in the identification cuts. ii. EmissT definition: As discussed in Section 3.2 and outlined in Equation (3.2), the total EmissT vector can be split into its true (E true T ) and fake (E fake T ) components. In SM processes, the only expected EtrueT is from neutrinos and anything else is considered EfakeT arising from experimental effects. From now on, the variable E miss T and it’s components EtrueT and E fake T will be assumed to represent those in Zνν + jets events and their primed versions (EmissT ′ , EtrueT ′ , EfakeT ′ ) those in γ + jets events. Hence, to simulate the EmissT in Zνν + jets events from the γ + jets sample, the 5Cross-checks have made to verify that the γ + jets contribution to the 0` SRs can be safely neglected (see Section D.2). Experimental Studies 117 following applies: EmissT =E true T +E fake T (5.1) = pT(γ1) +E fake T ′ (5.2) = pT(γ1) + E miss T ′ (5.3) Equation (5.2) follows since the prompt photon pT is used to simulate the E true T in Zνν events (E true T = pT(γ1)) and the same experimental effects are expected to contribute equally to EfakeT in both types of events (E fake T =E fake T ′ ). Equation (5.3) follows since EtrueT ′ ∼ 0 is expected in γ + jets events (although it would still be possible to have neutrinos in the event, e.g. from γ + b-jets). Some subtlety enters in the definition of the EmissT ′ due to the EmissT definition used in the 0` analysis (MET Simplified20 RefFinal, see Section 2.2.5), which does not explicitly reconstruct terms for photons or taus (as mentioned, the 0` analysis neglects these objects in the event selection). Given that ATLAS reconstruction ordinarily identifies clusters belonging to photons as jets as well, and furthermore photons may be misidentified as electrons (e.g. when a conversion track is present, see Section 2.2.5), the clusters corresponding to a prompt photon are typically calibrated as though they originated from electrons or hadronic jets. Particularly in the case of jets, the numerical inversion jet calibration scheme (EMJES) used in all the analyses up to Moriond’12 does not separately scale electromagnetic and hadronic clusters, but applies a single pT- and η-dependent scaling factor to all clusters. As the EMJES scaling factor is always larger than the corresponding electromagnetic scale, photon clusters can be weighted high relative to the energies that would be appropriate for genuine photons. Hence, a momentum imbalance is introduced, producing EfakeT ′ opposite in φ to the leading photon. While this EfakeT ′ can be substantial in magnitude, it is typically aligned with the leading jet in the event, and thus photon events tend not to pollute the 0` signal regions, due to a cut on such event configurations (“∆φ cut” in Table 5.14, see Section 5.4.2). This is clearly illustrated in Figure 5.6 where different EmissT algorithms are plotted and, although the effect on Zνν + jets events is negligible (Figure 5.6(a)), that in γ + jets is not (Figure 5.6(b)). Prior to Moriond’12, the solution to this problem was to simply use a different EmissT reconstruction algorithm as shown in Table 5.12, which calibrated all calorimeter clusters appropriately, either by discriminating clusters based on location rather than 118 Experimental Studies by object association (MET LocHadTopo), or by associating photons appropriately (MET Simplified20withTightPhotons RefFinal). For Moriond’12, to increase the consistency with the 0` analysis, the MET Simplified20 RefFinal definition was retained, but the contribution of the jet or electron matched to γ1 was removed from the EmissT calculation, rather than being partially cancelled by removing pT(γ1) (EtrueT = pT(γ1) in Equation (5.3)). This new procedure was found to be in agreement with the previous procedure, as shown in Figure 5.7. In summary, both the γ1-jet overlap removal and E miss T ′ redefinition can be regarded as being required for purely experimental reasons, while the EtrueT redefinition is intrinsic to the method. After the application of these requirements, the result is a suitable EmissT + jets sample which can be used for the ‘0` Object Definition and Event Selection’, described in the next Section. EmissT components in CR1a EmissT component Moriond’12 EPS’11 PLHC’11 Moriond’11 EfakeT MET Simplified20 RefFinal ” MET Simplified20 MET LocHadTopo withTightPhotons RefFinal EtrueT ∑ γ1-matched jets ” ” pT(γ1) and electrons Table 5.12.: Names of reconstruction algorithms used to compute EfakeT (the one used for Moriond’12 being the same as in the 0` analysis) and the meaning of EtrueT in CR1a throughout the different analysis rounds. 5.4.2. 0` Object Definitions and Event Selection As shown in Figure 5.4, the following requirements are the last needed to define CR1a, and are applied on the EmissT + jets sample defined in the previous Section. They are referred to as “0` Object Definitions and Event Selection” (and together simply as “0` Selection”) because they are exactly those defining the 0` SRs. As mentioned in Section 3.3, one of the advantages of the γ + jets sample is that the large statistics make it possible to apply the SRs selections directly, without needing extrapolations from looser cuts. i. 0` Object Definitions: These define the 0` requirements for jets, electrons, muons and EmissT , as well as overlap-removal procedures between these objects. The specific Experimental Studies 119 ϒ-­‐jet  Overlap  Removal   Υ+jets events ETmiss + jets events Υ+X events CR1a(SR1) events CR1a(SR2) events CR1a(SR3) events ETmiss  defini4on   (ETfake  and  ETtrue)   CR1a Object Definition 0l Selection 0l  Object  Defini4on   0l  Event  Selec4on   Figure 5.4.: Schematic chart outlining the additional steps needed to define CR1a. First, an additional object definition specific to CR1a is required (an overlap removal between the prompt photon candidate and jets in the event and a redefinition of the EmissT variable), after which an appropriate EmissT + jets sample is defined. At this point, the 0` object definitions and event selections can be applied directly, which finally results in the definition of the CR1a sample (one for each SR). CR1a events are the input for the TF to get the Zνν background estimate. The meaning of the variables and abbreviations in the diagram are specified elsewhere in the text. 120 Experimental Studies dR(trueBoson, jet) 0 0.1 0.2 0.3 0.4 0.5 0.6 (p b) /0 .0 06 Ge V σ -510 -410 -310 -210 -110 1 10 210 310 410 J0_dRjclosestγ ZJ0_dRjclosest Figure 5.5.: The distribution of the ∆R variable between the true vector boson V (V = Zνν , γ) and the closest reconstructed jet in V + jets MC before V -jet overlap removal. In the γ + jets case, before overlap removal, almost all events have the closest jet within ∆R < 0.2 because the γ is also reconstructed as a jet, while the Zνν + jets sample does not suffer from this problem. After overlap removal, these jets are discarded and the closest jet is then well separated from the boson. The MC is from PYTHIA samples listed in Section C.1. MET [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 1 0. 0 Ge V -110 1 10 210 310 LHTiiZ S20RFSUSYiiZ S20RFPHOTONiiZ -1L dt ~163 pb0 Dijet channel (a) MET [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 1 0. 0 Ge V 1 10 210 310 410 LHTa S20RFSUSYa S20RFPHOTONa -1L dt ~163 pb0 Dijet channel (b) Figure 5.6.: Effect of three different EmissT reconstruction algorithms on MC (a) Zνν + jets and (b) γ + jets in the PLHC’11 0` dijet channel (see Appendix C.2). ‘LHT’ is for MET LocHadTopo, ‘S20RFSUSY’ for MET Simplified20 RefFinal and ‘S20RFPHOTON’ for MET Simplified20withTightPhotons RefFinal (see Table 5.12). The MC is normalised to the PLHC’11 luminosity. Experimental Studies 121 MET Simplified20 [GeV] 0 200 400 600 800 100012001400160018002000 Ev en ts / 50 G eV 1 10 210 310 410 510 610 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A MET Simplified20 [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 D AT A / M C 0 0.5 1 1.5 2 2.5 (a) MET Simplified20withTightPhotons [GeV] 0 200 400 600 800 100012001400160018002000 Ev en ts / 50 G eV 1 10 210 310 410 510 610 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A MET Simplified20withTightPhotons [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 D AT A / M C 0 0.5 1 1.5 2 2.5 (b) MET’ Simplified20 [GeV] 0 200 400 600 800 100012001400160018002000 Ev en ts / 50 G eV 1 10 210 310 410 510 610 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A MET’ Simplified20 [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 D AT A / M C 0 0.5 1 1.5 2 2.5 (c) MET’ Simplified20withTightPhotons [GeV] 0 200 400 600 800 100012001400160018002000 Ev en ts / 50 G eV 1 10 210 310 410 510 610 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A MET’ Simplified20withTightPhotons [GeV] 0 200 400 600 800 1000 1200 1400 1600 1800 2000 D AT A / M C 0 0.5 1 1.5 2 2.5 (d) Figure 5.7.: Moriond’12 Comparison of different EmissT algorithms from Moriond’12 (specified on the x-axis) in the γ+X sample. The definitions are as follows: MET Simp20: standard SUSY definition, photons not explicitly reconstructed. MET Simp20wTP: SUSY definition, but identifying tight photons and calibrating their clusters appropriately. METp Simp20: as for MET Simp20, but with the contribution of a jet or electron matched to γ1 removed. METp Simp20wTP: as for MET Simp20wTP, but with the contribution of γ1 removed. In (a) and (b), a noticeable tail is visible. This is due to backgrounds with genuine EmissT from a W → eν decay, where the electron fakes a photon. The broadening of the EmissT spectrum due to the miscalibration of photon clusters is also evident. After removing the photon contribution, the resulting simulated EmissT distribution is mostly independent of the reconstruction algorithm, as demonstrated in (c) and (d). Figures (c) and (d) hence represent the Zνν-like E miss T to be used for the subsequent 0` selection. 122 Experimental Studies object definitions have evolved throughout the different analysis rounds, and the details can be found in the corresponding analysis documentation [63,100–102] (see also Section 2.2.5 for a general overview). ii. 0` Event Selection / SRs: The 0` SRs are ultimately defined by cuts on a discriminating variable called the effective mass meff . For a channel which selects events with n jets, meff is defined to be the scalar sum of the transverse momenta of the leading n jets together with EmissT : meff(incl.) ≡ n∑ i=1 |p(i)T |+ EmissT , (5.4) Hence, through this variable, stringent requirements on EmissT and jets can be applied, which is why it is a powerful discriminant between SUSY signals and most SM backgrounds. The 0` SRs have evolved throughout the different analysis rounds and the details can be found in the corresponding analysis documentation [63,100–102]. For Moriond’12 six inclusive channels are defined (labelled A, A’, B, C, D and E), characterised by increasing jet multiplicity from 2 to 6 (except for A’ which has the same multiplicity as A but is differentiated by a different value of the EmissT to meff ratio). The lower jet multiplicity channels target models of squark pair production with short decay chains, while the high jet multiplicity channels target gluino pair production and/or long cascade decay chains (see Section 1.2.3). The corresponding SRs are summarised in Table 5.13 and shown in full detail in Table 5.14. For the latter, Cuts 3a-5 are for “event cleaning” due to a variety of experimental effects and data- taking conditions (Section 5.2.1), so the actual discriminating cuts only start from Cut 7 onwards. In order to make this distinction, the expression ‘0` preselection’ will be used to refer to the application of all cuts up to and including Cut 6 (“0` veto”). Cut 14 is the“∆φ cut” – a requirement on the smallest of the azimuthal separations between the EmissT vector and the reconstructed jets. For channels A, A’ and B, the selection requires ∆φ > 0.4 using up to three leading jets. For the other channels an additional requirement ∆φ > 0.2 is placed on all jets with pT > 40 GeV. Requirements on ∆φ and EmissT /meff (Cut 15) are designed to reduce the background from multi-jet processes. The last cut (Cut 16) uses “meff(incl.)” rather than meff , which sums over all jets with pT > 40 GeV, as it has been found to improve the QCD jet background rejection [100]. Experimental Studies 123 In summary, to define CR1a, all the requirements from Table 5.14 have to be applied on the EmissT + jets sample previously defined, with the exception of Cut 2 (a different trigger requirement was already applied when defining the γ + X sample in Section 5.3). Since there is more than one SR, the result is one CR1a sample per SR. From now on, unless otherwise stated, the expression ‘CR1a sample’ will be frequently used to refer to all these CR1a samples, rather than just one. Similarly, the expression ‘0` selection’ will be used to refer to the combined ‘0` object definition and event selection’. This concludes all the addtional object definitions and event selections required by the method, since the CR1a sample is what is needed to calculate the TF and get the Zνν + jets background estimate. Therefore, the remainder of this Section is dedicated to discussing a few results and features observed in the CR1a sample. Requirement Channel A A’ B C D E EmissT [GeV] > 160 pT(j1) [GeV] > 130 pT(j2) [GeV] > 60 pT(j3) [GeV] > – – 60 60 60 60 pT(j4) [GeV] > – – – 60 60 60 pT(j5) [GeV] > – – – – 40 40 pT(j6) [GeV] > – – – – – 40 ∆φ(jeti, E miss T )min > 0.4 (i = {1, 2, (3)}) 0.4 (i = {1, 2, 3}), 0.2 (pT > 40 GeV jets) EmissT /meff(Nj) > 0.3 (2j) 0.4 (2j) 0.25 (3j) 0.25 (4j) 0.2 (5j) 0.15 (6j) meff(incl.) [GeV] > –/1400/1900 –/1200/– –/–/1900 900/1200/1500 –/–/1500 900/1200/1400 Table 5.13.: Moriond’12 analysis 0` channels (where the SRs are defined by the last cut). Note that meff constructed from the leading N jets is used in the E miss T /meff cut while that constructed from all jets with pT > 40 GeV is used for the final meff(incl.) cut. The three meff selections listed in the final row denote the ‘loose’, ‘medium’ and ‘tight’ selections respectively (but not all channels possess three SRs). 5.4.3. Comparison with SM prompt photon results In Section 5.3.4, the SM analysis results (Appendix B) were shown to apply to the γ +X sample. This was of course expected, given the identical object definitions and event 124 Experimental Studies Cut Description Channel A A’ B C D E 1 DQ (data) Run / lumi block appears in SUSY GRL data11 7TeV.periodAllYear DetStatus-v36-prod10 CoolRunQuery-00-04-08 Susy.xml 2 Trigger EF j75 a4 EFFS xe45 loose noMu (data period B) / EF j75 a4tc EFFS xe45 loose noMu (K ≥ data period ≥ D) / EF j75 a4tc EFFS xe55 noMu (data period ≥ L) / None (MC) 3a Ev. clean No Looser bad jets after jet-lepton overlap - jets (data) removal with pT > 20 GeV and any η 3b Ev. clean - jets Reject if leading up to 2 selected jets with pT > 100 GeV after overlap removal (data and MC) possess (chf < 0.02 and |η| < 2.0) or (chf < 0.05 and emf > 0.9 and |η| < 2.0) 3c Ev. clean - jet Energy-weighted mean time of leading N selected jets after timing overlap removal in N jet analysis |〈t〉| < 5 ns. 3d Ev. clean - LAr hole ‘Smart’ LAr hole veto 3e Ev. clean No selected muons after overlap removal with - cosmics (fabs(mu staco z0 exPV) ≥ 1) or (fabs(mu staco d0 exPV) ≥ 0.2) 3f Ev. clean No selected muons before overlap removal with Bad muon veto sqrt(mu staco cov qoverp exPV)/fabs(mu staco qoverp exPV) ≥ 0.2 3g Bad MET MUON Veto event if (MET MUON/EmissT )× cos(MET MUON phi−MET phi) > 0.5 3h Ev. clean Veto event if any selected jet with pT > 40 GeV and BCH CORR JET > 5% Bad tile drawers satisfies ∆φ < 0.2 3i Bad MET CellOut Veto event if (MET CellOut/EmissT )× cos(MET CellOut phi−MET phi) > 0.5 4 Ev. clean - LAr (data) larError == 0 5 Ev. clean - Prim. vtx. Leading primary vertex with > 4 tracks 6 Lepton veto No selected e/µ after overlap removal with pT > 20/10 GeV. 7 EmissT [GeV] > > 160 8 pT(j1) [GeV] > 130 9 pT(j2) [GeV] > 60 10 pT(j3) [GeV] > – – 60 60 60 60 11 pT(j4) [GeV] > – – – 60 60 60 12 pT(j5) [GeV] > – – – – 40 40 13 pT(j6) [GeV] > – – – – – 40 14 ∆φ(jeti, E miss T )min > 0.4 (i = {1, 2, (3)}) 0.4 (i = {1, 2, 3}), 0.2 (pT > 40 GeV jets) 15 EmissT /meff(Nj) > 0.3 (2j) 0.4 (2j) 0.25 (3j) 0.25 (4j) 0.2 (5j) 0.15 (6j) 16 meff(incl.) [GeV] > –/1400/1900 –/1200/– –/–/1900 900/1200/1500 –/–/1500 900/1200/1400 Table 5.14.: Full version of Table 5.13 detailing the event selection, including “event cleaning” cuts. The SRs are defined by cut 16. The main variables are defined elsewhere in the text and the rest in [100]. Experimental Studies 125 selections used up to that point. However, in the CR1a sample the validity of these results is not immediately obvious. Although the photon acceptance and efficiencies are mainly determined by the γ +X selection, some minor effects from the 0` selection in CR1a could be expected. However, as the 0` selection emphasises hard jet activity balanced by the total EmissT vector (i.e. mainly the boson pT in the case of CR1a and Zνν + jets), it predominantly selects events with hard photons that are well-separated from the leading jets. Hence, in principle no photon reconstruction biases should be introduced by such selection. It is therefore reasonable to compare the photon acceptance and efficiency in CR1a with the SM analysis results. Supporting cross-checks were done, in particular for the first analysis rounds when the method was being validated, to show this assumption was acceptable. In fact, for the Moriond’11 analysis, part of the Z/γ TF (e.g. Aγ · εγ and purity) used the SM analysis results directly (see Section C.1). As an example, Figure 5.8 shows the effect of the 0` selection on a shower shape Fside (the fraction of the energy deposited in the first layer of the ECAL, in seven strips centred around the first maximum that is not contained in the three core strips [48]) which is relevant to εγid. This shows that the 0` selections have a rather beneficial impact on εγid since slightly higher values are expected from the resulting narrower shape. Therefore, the value of εγid taken from the SM analysis would be rather conservative on CR1a. An equivalent comparison for a different shower shape variable is shown in Appendix C.1.4. The overall lack of data/MC agreement in shower shapes had already been observed in the SM analyses, e.g. see [49], and understood to be the result of MC mismodelling, for which correction factors based on the average differences with respect to data were applied in their estimation of εγid. 5.4.4. Results The Moriond’12 numbers of events in data passing the full CR1a selection for the various SR channels are quoted in Table 5.15. The good statistics of CR1a are evident and this nice feature is more obvious when comparing it with the other 0` CRs (see Section 5.6.2). The corresponding pT(γ1) distributions for the loosest SR per channel are shown in Figure 5.9, where the expected high purity is suggested by the MC. The pT(γ1) range and average across all channels is specified in Table 5.16 and compared to those in previous analyses. The CR1a meff distributions (prior to Cut 16) for each channel are shown in Figure 5.10, compared to ALPGEN MC (the distributions for the SRs and other CRs can be found in 126 Experimental Studies 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_fside [GeV] En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD J2_ph_fside [GeV] En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD J2MET_ph_fside [GeV] En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (c) Figure 5.8.: PLHC’11 Effect of the 0` selections on a shower shape distribution used for the “tight” identification Fside: (a) γ +X sample; (b) E miss T + jets sample with 0` Dijet selection and (c) EmissT + jets sample with 0` Dijet selection and E miss T cut (the E miss T + jet sample is as defined in Figure 5.4). The MC shown is from PYTHIA (Section C.1.2). Experimental Studies 127 [100]). A slight difference in the slopes of the meff(incl.) distributions can be observed, which is believed to be due to ALPGEN mismodelling of the photon pT and/or hadronic activity. When the hard cuts on EmissT and E miss T /meff are applied, this causes the MC to overshoot the data [100]. For the purpose of presentation of the Moriond’12 plots, data-driven scaling factors were applied to the MC to match the data in all the SRs and other CRs, except for CR1a and CR2. In the case of CR1a, this was because the data-MC agreement was considered good enough; whereas for CR2 it was because the corresponding background estimate (QCD/multi-jet) was mostly data-driven. As will be discussed in Section 5.6, these scaling factors have no impact on the final Moriond’12 0` results because the background normalisation was handled by a fit to data. Moriond’12 CR1a Event Counts SR A A’ B C D E meff(incl.) cut [GeV] 1400 1900 1200 1900 900 1200 1500 1500 900 1200 1400 CR1a / Z/γ+jets 81 9 155 6 201 45 6 3 74 24 10 Table 5.15.: Moriond’12 CR1a data event counts for all 0` SRs. CR1a pT(γ1) Moriond’12 EPS’11 PLHC’11 Moriond’11 Range [GeV] 85-1410 85-960 70-590 50-550 Average [GeV] 296-889 225-509 220-460 250 Table 5.16.: Ranges and average values of the prompt photon pT in all the CR1a samples (one CR1a per SR) in the different analysis rounds. The corresponding distributions for Moriond’12 are shown in Figure 5.9. For illustration, the event display of the event with the highest value of pT(γ1) and meff(incl.) entering CR1a A, A’ and B is shown in Figure 5.11, indicating that this event is most likely a genuine prompt photon event, and not due to fake sources like non-collision backgrounds. The event displays and details of all other events in this dataset with pT(γ1) > 1 TeV are shown in Appendix A.1. Having obtained the CR1a event sample, it is now possible to proceed to the next stage of the method, which is its conversion into a Zνν + jets background estimate. This is done with the Z/γ TF, which is the subject of the next section. 128 Experimental Studies [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 310 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-A [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (a) [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 310 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-Ap [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (b) [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-B [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (c) [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-C [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (d) [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-D [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (e) [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 Ev en ts / 50 G eV 1 10 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total + jets (Sherpa)γ + jets (Sherpa)γV Z+jets W+jets and single toptt InternalATLAS CR1a SR-E [GeV] T Photon p 0 200 400 600 800 1000 1200 1400 D AT A / M C 0 0.5 1 1.5 2 2.5 (f) Figure 5.9.: Moriond’12 CR1a prompt photon pT distributions for the loosest SRs per channel (A: 1400, A’: 1200, B: 1900, C: 900, D: 1500, E: 900). All selection criteria in Table 5.14 have been applied applied. The MC is from ALPGEN and the normalisation is to the data luminosity. Experimental Studies 129 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-A (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (a) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-Ap (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (b) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-B (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (c) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-C (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (d) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-D (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (e) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-E (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (f) Figure 5.10.: Moriond’12 CR1a meff(incl.) distributions. All selection criteria in Table 5.14 prior to the final meff(incl.) cut have been applied. The MC is from ALPGEN and the normalisation is to the data luminosity. 130 Experimental Studies Figure 5.11.: Moriond’12 Event display of the highest pT(γ1) event (1407 GeV) entering CR1a A, A’ and B. There is a single photon of good quality, and the jets in the event are similarly good. The leading jet in the collection is that reconstructed from the photon clusters, and is over-calibrated to have pT = 1645 GeV. This over-calibration generates most of the the E miss T , which points opposite to the photon, and aligns perfectly with the second leading jet (leading hadronic jet). More details of this event can be found in Table A.1. Experimental Studies 131 5.5. Transfer Function (TFZνν) In the 0` analysis, the measurements in the CRs are used to derive background expec- tations in a SR through the use of Transfer Functions (TFs). Technically, the TFs are defined as the ratio of expected event counts in the CRs and SR, and also between CRs (to estimate CR contamination by other SM processes). The TF therefore provides a conversion factor of “SR events per CR event”, as expressed by the equation: N(SR, est, proc) = N(CR, obs, proc) · TF = N(CR, obs, proc) · [ N(SR, raw, proc) N(CR, raw, proc) ] , (5.5) where N(SR, est, proc) is the SR estimate for a particular background process, N(CR, obs, proc) is the observed number of data events in the CR for the calibrating process chosen, and N(SR, raw, proc) and N(CR, raw, proc) are “raw” estimates of the contributions from the processes in the SR and CR respectively6. Similar equations containing TFs from CR to CR (“cross-TFs”) enable the background estimates to be normalised coherently across all the CRs (Section 5.6.1). The TFs are estimated using data-driven techniques wherever possible, otherwise MC simulation is used. Given that the TF is a ratio, it has the advantage of having some systematic uncertainties largely cancelling, e.g. that on the Jet Energy Scale (JES) in MC. In this thesis, the SR background component of interest is Zνν + jets and the CR is CR1a. As presented in Section 3.4, the corresponding Zνν/γ TF is defined as: TFZνν (pT) = P (pT) Aγ(pT) · εγ(pT) ·RZ/γ(pT) ·Br(Z → νν) (5.6) To properly account for the effects of the 0` object and SR event selection, this TF has to be evaluated after the full CR1a selection (Sections 5.3-5.4): NZνν (SR, pT) = TFZνν (SR, pT) ·Nγ(CR1a, pT) (5.7) The procedure can hence be regarded as a map from the CR to the SR, as illustrated in Figure 5.12. For brevity, from now on “TF” will be often used to refer to that from CR1a. 6These raw estimates need not be normalised to any particular luminosity or calibrated to other physics processes, but should be weighted by cross-section, and the normalisation convention should be consistent between SR and CR. 132 Experimental Studies Figure 5.12.: Schematic diagram showing the effect of the TF as a map from an ‘ideal’ CR to a SR or to another control region CR′ (the latter case is referred as a ‘cross-TF’). The ‘ideal’ TF would be fully calculated from data. Being a ratio, the TF has the advantage of cancelling some of the associated systematics errors. The next subsections will be dedicated to explain the method for estimating each of the factors in Equation (5.6) and their associated systematic uncertainties (in order of appearance). 5.5.1. Efficiency and Acceptance The Aγ(pT) · εγ(pT) factor in the TF is needed to correct for the effects from the γ +X selection in CR1a, which are absent from the Zνν + jets background events in the SRs. Rather than obtaining the acceptance and efficiencies separately, a single Aγ(pT) · εγ(pT) function is obtained from prompt photon MC by taking the ratio of the pT(γ1) distributions in CR1a with and without the γ +X selection step applied, i.e. : Aγ(pT) · εγ(pT) = N γ reco(pT) Nγtruth(pT) . (5.8) When the γ +X selection is not included, the truth photon four-vector is used for γ1-jet overlap removal, and to define EtrueT (Equations 5.1-5.3). The ALPGEN A γ(pT) · εγ(pT) function in each channel at different stages of the CR1a selection is shown in Figure 5.13, where the yellow/orange (bottom) line is the closest to the full CR1a selection (a common 900 GeV meff cut is used instead of the SR cut one to maintain reasonable statistics). The results were cross-checked with SHERPA and very good agreement was found. For complementary purposes, to get an idea of how much acceptance is lost from the photon η cuts in the γ +X selection step (see Table 5.8), an example of the estimated value of Aγ alone is shown in Table 5.17 for the relevant pT(γ1) range in channel A (see Figure 5.9(a) and Table 5.16) and for the two selected |η| regions used in the SM analysis [48,49]. From this, it is clear the loss is less than ∼ 10%. Given the practically flat |η| distribution (Figure 5.2(b)), both estimates are clearly consistent with each other. Experimental Studies 133 Analysis |η| region CR1a 〈Aγ(pT)〉 for SR-A All others < 2.37 0.92-0.96 Moriond’11 < 1.81 0.74 Table 5.17.: Mean acceptance of true photons for the η cuts used in [48, 49]. The first applies to all analyses except Moriond’11. Comparison with SM prompt photon results Identification and reconstruction efficiencies (εγrec, ε γ id) - As suggested by the dis- cussion in Section 5.3.4, the combined efficiency εγrec · εγid is relatively constant for high-pT photons, such as those selected in CR1a. Although the efficiency varies slightly between the central and forward η regions, this only implies an effect of ∼ 2% on the overall value, which according to the results from the SM analysis is ∼ 86%, close to the high-pT values seen in Figure 5.13 (black line). Isolation efficiency (εγiso) - As mentioned in Section 5.3.4, this efficiency is not calcu- lated explicitly in the SM analysis but becomes important here at this stage. The efficiency of the isolation requirement εγiso tends to decrease with increasing hadronic activity, which is amplified when requiring more reconstructed jets or a higher photon pT – both requirements of the 0` selection and particularly accentuated in Moriond’12. While the required separation between the EmissT and jets in the 0` selection (∆φ cut in Table 5.14) implies an isolated photon, the requirement is not as hard as the EisoT cut used (see Section 5.3.1). Therefore, the net effect is a reduced εγiso, which must be estimated in this specific context. This was done by comparing with the EisoT distribution from prompt photon MC passing the 0` selection but bypassing the γ +X selection (again, truth photon information was used for the 0` selection in this case). Typical values were found to be between 80% and 90%. As discussed in Section 5.3.4 a slight data/MC disagreement was observed in the EisoT distribution (Figure 5.1(b)), consistent with a ∼ 2 GeV ‘shift’. To understand this difference, the efficiency of two different EisoT cuts (3 and 5 GeV) was studied using the γ +X sample, and the resulting discrepancy between the data and MC was used to set an uncertainty estimate on εγiso. In the Moriond’12 analysis, a preliminary estimate determined that the discrepancy was under 5%, and this figure was hence set as the relative uncertainty. On repetition of the investigation with 134 Experimental Studies leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RA ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (a) leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RA p ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (b) leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RB ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (c) leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RC ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (d) leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RD ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (e) leading photon pT 0 200 400 600 800 1000 1200 1400 1600 1800 2000 ph ot on e ve nt s / 5 0 G eV -110 1 10 210 310 410 510 610 710 810 InternalATLAS [GeV] T leading photon p 0 200 400 600 800 1000 1200 1400 1600 1800 2000 (re co / t rut h), S RE ε × A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 InternalATLAS 85 GeV photon Isolated photon SUSY preselection cuteffBefore M >900effM (f) Figure 5.13.: Moriond’12 distributions of truth and reconstructed pT(γ1) (upper plot) and their ratio Aγ(pT) · εγ(pT) (lower plot) at different CR1a selection stages in every 0` channel (A, A’, B, C, D, E) – black line: all cuts from Table 5.9 and the signal photon definition without isolation applied; blue line: all cuts from Table 5.9 and the full signal photon definition applied (‘signal photons’ are defined in Section 5.3.1); green line: 0` preselection (as defined in Section 5.4.2); red line: full 0` selection except the meff(incl.) cut; orange line: full 0` selection including a 900 GeV meff(incl.) cut. In the upper plot, dashed lines indicate the truth photon distributions and solid lines the reconstructed ones. The MC is from ALPGEN and normalised to the data luminosity. Experimental Studies 135 some analysis improvements, the difference was found to be slightly larger as quoted in Table 5.18. This slight shift in EisoT and shower shapes (e.g. Figure C.3) was also observed in the SM analysis [49]. Signal Region Isolation efficiency, εγiso Relative difference, EisoT > 3 GeV E iso T > 5 GeV δε A 0.825 0.885 6.8% A’ 0.838 0.877 4.4% B 0.807 0.865 6.7% C 0.796 0.851 6.6% D 0.758 0.824 8.0% E 0.740 0.819 9.6% Table 5.18.: Moriond’12 efficiency of the EisoT cut (ε γ iso), evaluated in CR1a (but with a 900 GeV meff(incl.) cut applied in all cases) for thresholds of 3 and 5 GeV. The relative difference (with respect to the 5 GeV isolation criteria) determines the uncertainty. The values are taken from ALPGEN. An overall comparison is then made between the acceptance Aγ and efficiencies εγrec · εγid from[49] combined with the εγiso computed above, and the A γ(pT)·εγ(pT) bin-by-bin results computed from ALPGEN MC (Figure 5.13). The difference between the two estimates at high pT, where the ratio is approximately constant, is taken as the final uncertainty (see Table 5.20), and comes out to be significantly larger than the detailed estimates from the SM analysis. The uncertainty with respect to pile-up on Aγ(pT) · εγ(pT) is always estimated as in the rest of 0` analysis (for Moriond’12 this is specified in [100], but see also Section 5.5.5). In summary, the fact that the SM analysis results agree well with those obtained for CR1a confirms the relatively small impact from the 0` selection step, particularly in the important regime of high photon pT. This is clearly shown in Figure 5.13, where after the application of the EisoT cut (blue line), A γ(pT) · εγ(pT) remains fairly constant (within statistical uncertainties) with respect to the 0` selection. In particular, the final meff(incl.) cut does not lead to large shifts (only at the highest jet multiplicities is the difference greater than 5%). Applying the meff(incl.) cut does move the A γ(pT) · εγ(pT) plateau region to higher values of pT, but Figure 5.14 shows that the total effect once combined with RZ/γ is not so substantial. From this and to improve the statistics available, no meff(incl.) cut was applied when computing the value of A γ(pT) · εγ(pT). In addition, as Aγ(pT) · εγ(pT) is expected to flatten out at high pT, a plateau value was used in the 136 Experimental Studies TF for pT > 400 GeV in SRs A, A’, B and for pT > 350 GeV in SRs C, D, E to reduce the impact of statistical fluctuations. For clarity purposes, the plateau line is not shown directly in Figure 5.13 but an equivalent plot displaying it can be found in [100]. 5.5.2. Purity This TF component is not determined directly in these studies for two main reasons: (i) more thorough data-driven estimates have been carried out in the SM analysis already [49,99], and (ii) the purity of the CR1a sample is expected to be already quite high at this stage. As discussed in Section 5.3.4, the purity indeed increases with pT and the background suppression is mainly related to EisoT . From MC, QCD is estimated here to contribute 1% to the selected sample for pT ∼ 200 GeV and 0% for pT > 300 GeV. This is consistent with the good agreement between photon data and the MC signal in CR1a (Figure 5.9), which in addition supports the conclusion that the background is not significantly increased by the 0` selection. Reference [99] found the electron background to be ∼ 1%, which agrees with the MC estimate of electroweak processes in Figure 5.9. Therefore, because the total contamination is expected to be only at the percent level, it is not explicitly accounted for in the Zνν background estimation. Instead, a 5% uncertainty is assigned, based on the maximum background fraction estimated in [49] within the bulk of the photon pT distribution in CR1a (mean values are specified in Table 5.16). The reason to prefer a purity estimate based on [49] over a direct estimate from MC is because the former uses more sophisticated, e.g. data-driven, methods to estimate it and has much smaller associated uncertainties. 5.5.3. Z/γ Ratio The uncertainties related to the cross section ratio RZ/γ have been studied in [56] and were summarised in Chapter 4. The key point from these studies is that many of the theoretical uncertainties, such as the choice of scales and PDFs, are found to largely cancel in the ratio (net impact is less than ∼ 5%). It was, however, also shown that this ratio can be sensitive to jet selections and that multi-parton matrix elements should be used to correctly describe all the relevant amplitudes. For Moriond’12, the availability of more suitable MC samples than in the previous analyses made it possible to estimate RZ/γ from fully-simulated ATLAS MC from SHERPA and ALPGEN. For both generators, 4 to 5 additional partons, besides the boson, in the Experimental Studies 137 matrix-element were simulated (see Section 5.2.2). However, the limited amount of statistics at high pT in these samples, in combination with the large number of required jets, did not allow for the ratio to be determined with a precision better than ∼ 25%. Moreover, the Z boson SHERPA samples were not only more statistically limited but also a disagreement with respect to data was observed for the leptonic (Z``) samples e.g. when compared to CR1b (see SHERPA CR1b meff plots in [100]). This was thought to be the reason why the RZ/γ value computed from SHERPA was found lower than the theoretical expectation from [56]. Hence, for the TF, RZ/γ was determined with the ALPGEN samples, which suffered from neither of these problems. The results is shown in Figure 5.14, where the robustness and convergence of RZ/γ with respect to different selections at high pT is observed (although the specific threshold for this varies, depending on the meff(incl.) cut). The large RZ/γ values after the 0` preselection (black line) in the lowest bins are due to generator-level cuts on the photon MC, not applied to the Zνν MC (see Section 5.2.2). However, the effect vanishes after application of the EmissT cut (Cut 7 in Table 5.14). The results were also found to roughly be in good agreement with [56] (see Figure 3.1(b) and Table 4.1). Differences between the selection stages are comparable to the MC statistical fluctuations of the ratio at high pT, for which a 25% theoretical uncertainty is assigned to cover such effects. It should be noted that no NLO/NNLO k-factor was applied when normalising either the photon or Z samples to cross-section. This partly was because no such k-factor was available for the photon sample, but more importantly it is expected that, because the processes are so similar, any higher-order effects will cancel out in the ratio7, and so the normalisation to data should sufficiently account for these effects. The relevance of the k-factor is discussed further in Section 5.5.4. As RZ/γ flattens out at high pT, a plateau value was also used as for Aγ · εγ in the TF for pT > 500 GeV in SRs A, A’, B, for pT > 400 GeV in SR C, and for pT > 350 GeV in SRs D and E to reduce the impact of statistical fluctuations. For clarity purposes the plateau line is not shown in Figure 5.14 but is displayed on the equivalent plot in [100]. It is worth noting that prior to Moriond’12, RZ/γ was taken directly from the result in [56] (which used PYTHIA8 and GAMBOS). This approach, however, was not entirely adequate given the hard scales and high multiplicities characterising the 0` selections, in particular that in Moriond’12. The RZ/γ taken from [56] did not include the effects of the exact 0` selection, nor of drawing on the full ATLAS simulation. During this time, the overall uncertainty quoted on RZ/γ was ∼ 15% (see Appendix C). 7Except perhaps for the Sudakov-type corrections, see Section 4.5. 138 Experimental Studies γ vs Zνν Pseudorapidity While in principle the Z boson and γ have different η distributions, causing some visible differences in the event kinematics, the effects disappear at high pT (specifically pT  mZ) as the η distributions for the two bosons converge. Moreover, this is always ensured by the 0` selections, as exemplified in Figure 5.158. A similar figure with larger statistics at generator level from PYTHIA is shown in Figure 4.14(b). This is the reason to parameterise RZ/γ as a function of pT only, while the limited fiducial acceptance of the photons is accounted through the Aγ factor described previously. 8These plots correspond to the Moriond’11 selection, but the effect is expected to be more robust for the harder Moriond’12 selection. Experimental Studies 139 [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RA γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (a) [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RA p γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (b) [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RB γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (c) [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RC γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (d) [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RD γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (e) [GeV] T Boson p 0 200 400 600 800 1000 1200 Ev en ts / 50 G eV -310 -210 -110 1 10 210 310 410 510 610 InternalATLAS [GeV] T Boson p 0 200 400 600 800 1000 1200 + jet s), S RE γ( σ (Z +je ts) / σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 InternalATLAS SUSY preselection meffincl > 0 meffincl > 900 meffincl > 1200 Acceptance-corrected Acceptance-corrected (f) Figure 5.14.: Moriond’12 distributions of truth Zνν and γ pT (upper plot) and their ratio RZ/γ(pT) (lower plot) at different CR1a selection stages in the 0` channels (A, A’, B, C, D, E). The hollow/smaller circles correspond to corresponding solid circles multiplied by the Aγ(pT) · εγ(pT) function in Figure 5.13. In the upper plot, dashed lines indicate the Zνν distributions and solid lines the γ ones. The MC is from ALPGEN and normalised to the data luminosity. 140 Experimental Studies (boson) [GeV]η -3 -2 -1 0 1 2 3 0.02 0.025 0.03 0.035 0.04 ννAlpgen Z γAlpgen (a) (boson) [GeV]η -3 -2 -1 0 1 2 3 0.02 0.025 0.03 0.035 0.04 0.045 ννPythia Z γPythia (b) (boson) [GeV]η -3 -2 -1 0 1 2 3 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 ννAlpgen Z γAlpgen (c) (boson) [GeV]η -3 -2 -1 0 1 2 30 0.01 0.02 0.03 0.04 0.05 0.06 ννPythia Z γPythia (d) (boson) [GeV]η -3 -2 -1 0 1 2 3 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 ννAlpgen Z γAlpgen (e) (boson) [GeV]η -3 -2 -1 0 1 2 30 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 ννPythia Z γPythia (f) Figure 5.15.: Moriond’11 pseudorapidity (η) distribution for true γ and Zνν at different CR1a selection stages, using reconstructed jets from PYTHIA and ALPGEN: (a)-(b) after the γ + X selection; (c)-(d) after the 0` dijet selection; and (e)-(f) after the 0` three jet selection. The histograms are normalised to unit area to facilitate comparison of shapes and the y-axis has arbitrary units. Experimental Studies 141 5.5.4. Application of TF/ TF stand-alone estimate of Zνν + jets At this stage it is possible to obtain a ‘stand-alone’ estimate of the Zνν + jets background in the various SRs by simply applying the TF (Equation (5.6)) on the CR1a event counts. This is a less sophisticated procedure than the one actually implemented in the 0` analysis, in which the TFs of all the CRs are combined to produce a fit where all background processes are simultaneously normalised (see Section 5.6.3). However, by carrying out this more rudimentary approach, it is possible to immediately cross-check the method’s estimate directly against simulated Zνν + jets events. The relevant numerical results obtained from this cross-check are listed in Table 5.19 and the corresponding distributions are shown in Figure 5.16. The main results are the raw CR1a event counts (column 3) and the data-driven Zνν + jets events estimate (column 5). The latter is obtained from the integrated value of the distribution of black dots in Figure 5.16. This distribution is produced by filling a two-dimensional histogram of meff(incl.) vs pT(γ1), and then scaling the meff(incl.) projected histogram bin-by-bin in pT by the corresponding TF as in Equation (5.7). The rest of the results in Table 5.19 are just cross-checks made with MC to support the validity of the method. Z + jets data/MC discrepancies Within the 0` analysis, the Zνν + jets ALPGEN samples included a k-factor of 1.28 (see Table 5.4) to include NNLO corrections to the cross-section, and the SHERPA samples a k-factor of 1.20 owing to the running of αEM. However, these k-factors were not applied to this stand-alone Zνν + jets estimate since no equivalent k-factor was available for the γ + jets MC, but more importantly because the method is primarily data-driven (the MC dependance is based on a ratio where higher order corrections like these should cancel). The Zνν + jets ALPGEN distribution does appear on average higher than data, but this is related to a common trend observed for all the Z boson related ALPGEN samples used in the 0` analysis. For this, the 0` analysis applied a scale factor of 0.75 to the normalisation in order to improve the agreement with data, but this is not included in this estimate. As for the discrepancies of Zνν + jets SHERPA with data (columns 6 and 7 in Table 5.19), these were previously observed for RZνν/γ (Section 5.5.3) and are believed to be due also to an overall normalisation offset (i.e. SHERPA Z`` is found to be systematically lower than CR1b data [100]). In addition, given that Zνν + jets SHERPA sample is very statistics-limited at high meff(incl.), it is not considered reliable for counts below ∼ 10 events. 142 Experimental Studies The key point, however, is that these discrepancies with Zνν MC should not matter, given the data-driven nature of the result actually used for the final Zνν background estimate. (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region A (a) (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region A’ (b) (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region B (c) (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region C (d) (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region D (e) (incl.) [GeV]effm 0 500 1000 1500 2000 2500 3000 Ev en ts / 10 0 G eV -210 -110 1 10 210 310 410 Data 2011 estimate +jets Sherpa estimateγ +jets Alpgen estimateγ +jets SherpaννZ +jets AlpgenννZ -1 L dt = 4.7 fb∫ Signal Region E (f) Figure 5.16.: Moriond’12 Zνν + jets meff(incl.) distributions in the 0` SRs as estimated from data and MC using the CR1a TF, compared directly with Zνν + jets MC from SHERPA and ALPGEN. The labels ‘Data 2011’ and ‘γ + jets Sherpa/Alpgen estimate’ indicate the TFs were applied to the CR1a data and MC events, whereas those labeled ‘Zνν + jets Sherpa/Alpgen’ show the raw MC prediction scaled to the data luminosity. Experimental Studies 143 S R m eff (i n cl .) C R 1a Z ν ν + je ts E st im at e Z ν ν + je ts S ig n al d a ta S h er p a/ A lp ge n d at a S h er p a/ A lp ge n S h er p a/ A lp ge n A 14 00 81 97 .2 / 95 .2 30 .6 ± 3. 4 (s ta t. ) ± 8. 1 (s y st .) 37 .2 / 36 .4 22 .3 / 44 .2 19 00 9 9. 54 / 9. 41 3. 44 ± 1. 15 (s ta t. ) ± 0. 91 2 (s y st .) 3. 64 / 3. 59 1. 81 / 4. 87 A ’ 12 00 1 55 1 79 / 18 2 60 .2 ± 4. 83 (s ta t. ) ± 16 (s y st .) 70 / 71 .3 35 .8 / 86 .2 B 19 00 6 6. 32 / 6. 59 2. 49 ± 1. 02 (s ta t. ) ± 0. 66 4 (s y st .) 2. 59 / 2. 69 1. 28 / 2. 53 C 90 0 2 01 2 30 / 20 4 62 .7 ± 4. 42 (s ta t. ) ± 16 .7 (s y st .) 73 .5 / 64 .5 70 .4 / 80 .6 12 00 45 57 .4 / 46 .2 15 .2 ± 2. 26 (s ta t. ) ± 4. 33 (s y st .) 19 .2 / 15 .5 15 .5 / 21 .3 15 00 6 14 .6 / 11 .5 2. 06 ± 0. 84 (s ta t. ) ± 0. 64 3 (s y st .) 4. 98 / 3. 94 4. 35 / 5. 89 D 15 00 3 11 .2 / 7. 17 0. 89 6 ± 0. 51 8 (s ta t. ) ± 0. 25 4 (s y st .) 3. 37 / 2. 17 3. 01 / 3. 64 E 90 0 74 76 .9 / 51 .9 20 .7 ± 2. 41 (s ta t. ) ± 5. 69 (s y st .) 22 .2 / 14 .3 17 .6 / 17 .6 12 00 24 15 .7 / 15 .5 7. 29 ± 1. 49 (s ta t. ) ± 2. 03 (s y st .) 5. 1 / 4. 58 6. 14 / 5. 82 14 00 10 9. 01 / 6. 69 3. 12 ± 0. 98 5 (s ta t. ) ± 0. 88 9 (s y st .) 2. 92 / 1. 99 2. 71 / 2. 34 T ab le 5. 19 .: M o ri o n d ’1 2 C R 1 a ev en t co u n ts in d a ta a n d M C fo r ea ch S R (c o lu m n s 3 -4 ) a n d th e st a n d -a lo n e es ti m a te o f Z ν ν + je ts ba ck gr o u n d in th e 0 ` S R s fr o m d a ta a n d M C (c o lu m n s 5 -6 ), co m pa re d to Z ν ν + je ts M C (c o lu m n 7 ). T h e M C st a ti st ic a l a n d lu m in o si ty u n ce rt a in ti es a re n o t sh o w n bu t ca n be a ss u m ed to be sm a ll e. g. th e lu m in o si ty u n ce rt a in ty is ∼ 3. 9% . 144 Experimental Studies 5.5.5. Summary of TF results and uncertainties A summary of the CR1a TF results and associated uncertainties is shown in Table 5.20. These, along with the raw CR1a event counts (column 3 in Table 5.19), are the main results provided to the 0` analysis, where they are used as inputs for the final combined background fit (Section 5.6). In Table 5.20, the “Central Value” represents the expected value of the TF, defined as the integral of a Zνν estimate histogram in the SR (Figure 5.16) divided by the integral of the corresponding CR1a histogram (Figure 5.10), i.e. 〈TFZνν 〉 = 〈NZνν (SR)〉 〈Nγ(CR1a)〉 = ∫∞ 0 TFZνν (pT) ·Nγ(CR1a) dpT∫∞ 0 Nγ(CR1a) dpT . (5.9) Equivalently, these are weighted averages of the TF, where the weight function is the differential cross-section in pT. As for the TF uncertainties, the procedures to calculate them were as discussed in Section 5.5. Other uncertainties assessed to be consistent with the rest of the 0` analysis, also appearing in Table 5.20, were: • JES/JER: Jet energy scale and jet energy resolution uncertainties were assessed using the standard ATLAS tools provided by the Jet/ETmiss working group [103] • Trigger: the corresponding trigger efficiency (g80 loose for Moriond’12, see Ap- pendix B.2) • Pileup: related to the usage of the standard ATLAS pileup reweighing tool, it was estimated from the difference between nominal 〈µ〉 and 〈µ〉 × 0.9 (see Section 5.2.2). The factor of 0.9 was estimated based on the data/MC mismatch observed for mc11b (see Table 5.7). • MET CellOut: The uncertainty on the energy of topoclusters which are not associ- ated to physics objects but that contribute to the missing energy (the “CellOut” term in Equation (2.11)). An additional 6.6% pileup uncertainty is also applied, as recommended by the Jet/ETmiss group. Experimental Studies 145 C R 1 a T F c e n tr a l v a lu e a n d u n c e rt a in ti e s S R A A ’ B C D E m eff (i n cl .) 14 00 19 00 12 00 19 00 90 0 12 00 15 00 15 00 90 0 12 00 14 00 C en tr al V al u e 0. 37 7 0 .3 82 0. 38 8 0. 41 4 0. 31 2 0. 33 7 0. 34 3 0. 29 9 0. 28 0 0. 30 4 0. 31 2 f b k g 5 % 5% 5% 5% 5% 5% 5% 5% 5% 5% 5% εγ i so 5 % 5% 5% 5% 5% 5% 5% 5% 5% 5% 5% A γ ·ε γ 5 % 5% 5% 5% 5% 5% 5% 5% 7% 7% 7% T h eo ry (R Z ν ν / γ ) 25 % 25 % 25 % 25 % 25 % 25 % 25 % 25 % 25 % 25 % 25 % J E S / J E R 1 .6 % 1 .9 % 1. 6% 3. 6% 2. 7% 10 .7 % 16 .6 % 10 .7 % 5. 0% 6. 8% 9. 2% T ri g ge r < 1 % < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% P il eu p < 1 % < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% < 1% M E T C el lO u t 0 .3 % 0 .4 % 0. 3% 1. 0% 0. 4% 0. 7% 0. 9% 1. 3% 0. 9% 1. 0% 1. 3% T ab le 5. 20 .: M o ri o n d ’1 2 C R 1 a T F ex pe ct ed va lu e fo r ea ch 0 ` S R , to ge th er w it h th e es ti m a te d a ss oc ia te d u n ce rt a in ti es . T h e m ea n in g o f th e te rm s a re ex p la in ed el se w h er e in th e te xt . T h e M C st a ti st ic a l u n ce rt a in ty is in cl u d ed in th e ‘T h eo ry (R Z ν ν / γ )’ u n ce rt a in ty . 146 Experimental Studies 5.6. Context within the 0` analysis This final section contextualises this background estimation method within the 0` analysis. The importance and performance of the method will be discussed, and in particular its performance will be compared with that of other CRs, especially CR1b which is the 0` alternative for Zνν + jets background estimation. For reference, the selections defining the various 0` CRs are detailed in Table 5.21. These have been designed to be as orthogonal as possible to minimise correlations between them and the backgrounds they aim to estimate. They are as close as possible to the SR to maintain adequate statistical weight, while minimising the uncertainties arising from extrapolations to the SRs. Another characteristic is their high purity with respect to the calibration process chosen, exceeding 50% in all cases [54]. In order to be consistent with the documentation in [100], in this section, the presen- tation of SR and CR results in tables will follow a different format to the one presented in previous sections of this chapter – the SRs will be presented in the following order: SRC loose, SRE loose, SRA medium, SRAp medium, SRC medium, SRE medium, SRA tight, SRB tight, SRC tight, SRD tight, SRE tight. 5.6.1. Overview of relevant 0` results A summary of the most important results (prior to interpretation) of the 0` analysis is now given. First, the data event counts in the various SRs and CRs are quoted in Table 5.22 (the CR1a row is equivalent to Table 5.15). A sample of the corresponding meff(incl.) distribution for the electroweak boson production CRs is shown in Figure 5.17 for channel A (a more comprehensive collection is available in [100]). Transfer factor summary Next, the central values of the TFs used to translate the CR event counts into SR background estimates are presented in Table 5.23. The values presented for CR1a are the expected values discussed in Section 5.5.5 (Table 5.20) modified by a scaling factor to account for the small Z(→ ee, µµ, ττ) + jets contamination in the SR (the basic CR1a TF discussed in Section 5.5 accounts only for Z(→ νν)). Such events can evade the lepton veto when the leptons are softer than the threshold for the veto (chosen to ensure adequate reconstruction quality), land outside the detector acceptance or are Experimental Studies 147 simply misidentified or misreconstructed. Hadronically decaying taus make up the largest fraction of this background, as they are resolved as hadronic jets, and furthermore contain a non-negligible real EmissT component due to the neutrinos from the tau decays. The scaling factor is simply computed from Z + jets ALPGEN MC as: RZ/Zνν = NZ→X(SR)/NZ→νν(SR) (5.10) and is applied to all CR1a TF values shown within this section. In the simultaneous normalisation scheme used by the 0` analysis, it is important also to account for cross-contamination from background processes other than the one that is being targeted. This is done by constructing “cross-TFs”, which are TFs from CR to CR. For illustration, the ones corresponding to SR A (medium) are shown in Table 5.24. By construction, TF(CR1a→ CR1a), TF(CR1b→ CR1b), TF(CR2→ CR2), etc., are equal to 1. As the background fraction in CR1a (fbkg) has been assumed to be negligible, TF(CRX→ CR1a) = 0, except for CR1b (see below), as shown by the first row in the Table. As for TF(CR1a → CRX), these are obtained by combining appropriate TFs from CR1a and CR1b as follows: TF(CR1a→ CRX) = NZ(CRX) Nγ(CR1a) = NZ(CRX) NZ(CR1b) · NZ(CR1b) NZ(SR) · NZ(SR) Nγ(CR1a) = TF(CR1b→ CRX) TF(CR1b→ SR) · TF(CR1a→ SR) ·RZ/Zνν . (5.11) e.g. for SR A (medium) in Table 5.24, TF(CR1a→ CR2) = 0.051 Given that a combined fit is used to simultaneously normalise all the background components in the 0` analysis (see Section 5.6.1), when combining CR1a and CR1b results, it has been preferred to avoid introducing too many cross-correlations, so that rather than using the CR1a-CR1b cross-TFs in the fit, they are connected only indirectly via their respective TFs to the SR. In the case of CR1a this makes particular sense as it does not involve any extrapolation from a soft-to-hard region and therefore does not benefit from “short-cutting” the extrapolation by using a soft-to-soft TF. The corresponding entries in Table 5.24 therefore appear empty (“-”). 148 Experimental Studies C u t C o n tro l R eg io n 1 a 1 b 2 3 4 1 A s fo r S R C u t 1 (m o d u lo a p p ro p ria te strea m fo r trig g er) 2 E F g 8 0 lo o se E F e2 0 m ed iu m (p erio d ≤ J ) A s fo r S R cu t 2 A s fo r C R 1 b A s fo r C R 1 b / E F e2 2 m ed iu m (d a ta p erio d K ) / (E F e2 2 v h m ed iu m 1 O R E F e4 5 m ed iu m 1 ) (p erio d ≥ L ) O R E F m u 1 8 (p erio d < J ) / E F m u 1 8 L 1 J 1 0 (p erio d ≥ J ) 3 a -5 A s fo r S R cu ts 3 a -5 , w ith lep to n trea ted a s jet w ith ch f = 1 , em f = 0 a n d ex clu d ed fro m |〈t〉| fo r C R 3 / 4 . C u t 3 g : sig n a l m u o n (s) u sed in cu t 6 a ex clu d ed fro m E m iss T fo r C R 1 b / 3 / 4 . C u t 3 h : E m iss T ’ fro m cu ts≥ 7 u sed in C R 1 a / 1 b . 6 a E x a ctly 2 O S selected A s fo r S R C u t 6 E x a ctly 1 selected sig n a l E x a ctly 1 selected sig n a l S M P h o to n selectio n sig n a l electro n s o r m u o n s: electro n o r m u o n electro n o r m u o n (see S ectio n 5 .3 ) p T (e) > 2 5 , 2 0 G eV w ith p T (e) > 2 5 G eV w ith p T (e) > 2 5 G eV o r p T (µ ) > 2 0 , 2 0 G eV o r p T (µ ) > 2 0 G eV o r p T (µ ) > 2 0 G eV 6 b – – – N o p T > 4 0 G eV sel.|η| < 2 .5 ≥ 1 p T > 4 0 G eV sel.|η| < 2 .5 jet w ith J etF itterC o m b N N ≥ 1 .8 jet w ith J etF itterC o m b N N ≥ 1 .8 6 c – 6 6 G eV < m (``) – 3 0 G eV < m T (`,E m iss T ) 3 0 G eV < m T (`,E m iss T ) < 1 1 6 G eV < 1 0 0 G eV < 1 0 0 G eV U se E m iss T ’ = p T (γ ) + E m iss T (S i m p l i f i e d 2 0 E m iss T ’ = – T rea t lep to n T rea t lep to n b elo w : w i t h T i g h t P h o t o n s R e f F i n a l ) E m iss T + p T (``) a s a jet a s a jet 7 -1 3 A s fo r S R cu ts 7 -1 3 1 4 S R cu t 1 4 N o cu t ∆ φ < 0 .2 : N o cu t N o cu t i={ 1 ,2 ,(3 )} (A , A ’, B ) / p T > 4 0 G eV jets (C ,D ,E ) 1 5 S R cu t 1 5 N o cu t S R C u t 1 5 N o cu t N o cu t 1 6 S R cu t 1 6 S R C u t 1 6 S R C u t 1 6 S R cu t 1 6 S R cu t 1 6 / 1 5 0 0 G eV (A / B (tig h t)) T ab le 5.21.: M o rio n d ’1 2 even t selectio n s d efi n in g th e 0 ` C R s. F o r S R cu ts referen ced , see T a ble 5 .1 4 . F ro m [1 0 0 ]. Experimental Studies 149 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets + jets (Alpgen)γV + jets (Alpgen)γ For ApprovalATLAS CR1a SR-A (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (a) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS CR1b SRA (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (b) 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS CR3 SRA (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A / S M 0 0.5 1 1.5 2 2.5 (c) Figure 5.17.: Moriond’12 meff(incl.) distribution in data and MC for (a) CR1a, (b) CR1b and (c) CR3 in channel A. Though the purity of CR1a is slightly worse than CR1b, the statistics are much better, especially once the meff(incl.) cuts are applied, while with respect to to CR3, although the statistics are comparable, the purity of CR1a is better at any given pT, since CR3 suffers from a relatively large tt¯ and single top contamination. From [100]. 150 Experimental Studies CR / Signal Region Process SRC SRE SRA SRA’ SRC SRE SRA SRB SRC SRD SRE loose loose medium medium medium medium tight tight tight tight tight SR 210 148 59 85 36 25 1 1 14 9 13 CR1a / Z/γ+jets 201 74 81 155 45 24 9 6 6 3 10 CR1b / Z/γ+jets 28 0 12 25 6 0 1 1 3 2 0 CR2 / QCD jets 192 243 30 16 42 67 4 5 10 11 29 CR3 / W+jets 234 57 77 178 60 25 10 8 16 13 13 CR4 / tt¯+ Single t 164 87 26 63 51 35 18 17 14 13 15 Table 5.22.: Moriond’12 data event counts in the SR and CRs for each channel. From [100]. CR / Signal Region Process SRC SRE SRA SRA’ SRC SRE SRA SRB SRC SRD SRE loose loose medium medium medium medium tight tight tight tight tight CR1a / Z/γ+jets 0.35 0.29 0.39 0.42 0.37 0.34 0.32 0.4 0.35 0.3 0.32 CR1b / Z/γ+jets 2.9 6.5 2.5 2.2 2.9 5 5.3 4.2 1.8 2.1 2.7 CR2 / QCD jets 0.0051 0.024 0.036 0.098 0.0026 0.026 0.0021 0.0013 0.0014 0.0028 0.021 CR3 / W+jets 0.36 0.74 0.31 0.19 0.2 0.39 0.25 0.14 0.16 0.26 0.26 CR4 / tt¯+ Single t 0.52 0.84 0.35 0.22 0.27 0.54 0.0055 0.0084 0.14 0.17 0.29 Table 5.23.: Moriond’12 summary of initial (pre-fit) central values of the CRs TFs in every channel. Rows indicate the calibrating region/process, while columns indicate the SR for which the estimate is being made. N.B. TFs from CR1a contain a scaling factor that accounts for the Z background from decays other than to neutrinos, and hence do not exactly match those from Table 5.20. From [100]. Region Main CR/Process CR1a / Z/γ+jets CR2 / QCD jets CR4 / tt¯+ Single Top CR3 / W+jets CR1b / Z/γ+jets CR1a 1 0 0 0 - CR2 0.051 1 0.4 0.19 0.31 CR4 0 0 1 0.071 0 CR3 0.02 0 0.46 1 0.12 CR1b - 0 0.032 0 1 SR 0.39 0.036 0.35 0.31 2.5 Table 5.24.: Moriond’12 initial (pre-fit) cross-TFs for SR-A medium. Columns indicate the calibrating region/process, while rows indicate the region for which the estimate is being made. The reason for the CR1a-CR1b cross-TFs being empty is explained elsewhere in the text. From [100]. Experimental Studies 151 Final 0` results The vulnerabilities from relying on pure MC has been stressed enough by now. Indeed, the full sophistication of the current 0` analysis lies in the use of the data-driven background estimation methods rather than MC. Consequently, this requires a more complicated procedure than simply applying the TFs to the CR event counts, as was done in Section 5.5.4. Rather, all the CR measurements (event counts, SR-to-CR and CR-to-CR TFs and associated uncertainties) are combined via a fitting procedure to produce a more sophisticated background estimate, which ensures consistency for all processes and accounts for mutual contamination. The final 0` results for Moriond’12 are quoted in Table 5.25. These comprise the data event counts and the predicted SM contributions in all SRs, broken down by process as well as in aggregate. For the SM contributions, values in parentheses indicate the initial MC estimates, i.e. before the combined fit9, while the other values are after the fit. The fitting procedure is based on a likelihood function built from the Poisson probability density function (pdf) describing the SR (PSR) and its CRs (PiR where i = W(CR3),T(CR4),Za(CR1a),Zb(CR1b),Q(CR2)) and a pdf describing the systematic uncertainties (CSyst): L(n|µ, b,θ) = PSR × PWR × PTR × PZRa × PZRb × PQR × CSyst. (5.12) The mean of a CR pdf is then defined as: λi(µ,b,θ) = µ · CSR→iR(θ) + ∑ j CjR→iR(θ) · bjR where the index j runs over all CRs, µ is the signal strength, bjR is the background j in Region R and CjR−>SR the TF of process j from region R to the SR. For example, the terms CQR→QR, CWR→WR, CZRa,b→ZRa,b, CTR→TR correspond to the diagonal entries in Table 5.24. The likelihood fit is explained in more detail in [63], including how the correlations in the uncertainties are handled. In general, Table 5.25 shows that the observed SR event counts do not deviate substantially from the predictions of the fit, except in some of the tighter SRs, where fluctuations in both directions are seen. To a certain extent, these may also be due to fluctuations in the CR data driving the SM expectations up or down, e.g. due to a lack of statistics at high meff , as in Figure 5.17(b). 9This is the reason for the large discrepancy in the QCD estimate, e.g. MC being generally inadequate to properly describe the extreme tails of the EmissT in QCD multijet events. 152 Experimental Studies In order to illustrate better which background components are the most significant in each of the SRs, Table 5.26 shows the fraction from the total SM expectation that each background process contributes (again, pre-fit values are shown in parentheses). From this table, it is clear that the Z + jets background (here predominantly irreducible Zνν + jets events) are amongst the largest contributions to the total event count, e.g. for SRs A medium, Ap medium, C medium, A tight, B tight and C tight, this process in fact represents the largest contribution, and the second largest for the remaining SRs (except for SR E loose and D tight). The overall trend is that this background becomes more dominant with decreasing jet multiplicity. Finally, the meff(incl.) distributions (prior to the meff(incl.) cut) of the SRs in data and MC (ALPGEN) are shown in Figure 5.18. The data represents the event counts in Table 5.25, while the MC, the values in parenthesis for each SM contribution (except for QCD where the data-driven estimate is quoted). The ALPGEN W + jets, Z + jets and tt¯+ jets distributions in the Moriond’12 analysis were scaled respectively by 0.75, 0.78 and 0.73, in addition to the normalisation to the data luminosity, in order to improve the agreement with the data. These scaling factors are within the expected range of systematic uncertainties and were determined by normalisation to all data in CR3, CR1b and CR4 respectively in channel A. As mentioned, the CR1a plots do not have such scaling. The scaling was only cosmetic for the relevant plots and has no impact on the final Moriond’12 0` results, as the background normalisation is handled by the likelihood fit. Overall, reasonably good agreement is observed between the data and the SM expec- tation (both the MC and fitted versions), with no significant excesses seen. P ro ce ss S ig n a l R eg io n S R C lo o se S R E lo o se S R A m ed iu m S R A p m ed iu m S R C m ed iu m S R E m ed iu m tt¯ + S in g le T o p 7 4 ± 1 3 (7 5 ) 6 6 ± 2 6 (6 4 ) 7 ± 5 (5 .1 ) 1 1 ± 3 .4 (1 0 ) 1 2 ± 4 .5 (1 0 ) 1 7 ± 5 .8 (1 3 ) Z / γ + je ts 7 0 ± 2 2 (6 1 ) 2 2 ± 6 .4 (1 3 ) 3 1 ± 9 .9 (3 4 ) 6 4 ± 2 0 (6 9 ) 1 7 ± 5 .9 (1 6 ) 8 ± 2 .9 (4 .4 ) W + je ts 6 2 ± 9 .3 (6 1 ) 2 3 ± 1 1 (2 3 ) 1 9 ± 4 .5 (2 1 ) 2 6 ± 4 .6 (3 0 ) 8 .1 ± 2 .9 (1 1 ) 5 .9 ± 3 (4 .7 ) Q C D je ts 0 .3 9 ± 0 .4 (0 .1 6 ) 3 .7 ± 1 .9 (3 .8 ) 0 .1 4 ± 0 .2 4 (0 .1 3 ) 1 e − 0 6 ± 0 .1 3 (0 .3 8 ) 0 .0 2 4 ± 0 .0 3 4 (0 .0 1 3 ) 0 .8 ± 0 .5 3 (0 .6 4 ) D i- B o so n s 7 .9 ± 4 (7 .9 ) 4 .2 ± 2 (4 .2 ) 7 .3 ± 3 .7 (7 .5 ) 1 5 ± 7 .4 (1 6 ) 1 .7 ± 0 .8 7 (1 .7 ) 2 .7 ± 1 .3 (2 .7 ) T o ta l 2 1 4 ± 2 4 .9 (s y s) ± 1 3 (s ta t) 1 1 9 ± 3 2 .6 (s y s) ± 1 1 .6 (s ta t) 6 4 .8 ± 1 0 .2 (s y s) ± 6 .9 2 (s ta t) 1 1 5 ± 1 9 (s y s) ± 9 .6 9 (s ta t) 3 8 .6 ± 6 .6 8 (s y s) ± 4 .7 7 (s ta t) 3 4 ± 4 .4 7 (s y s) ± 5 .5 7 (s ta t) D a ta 2 1 0 1 4 8 5 9 8 5 3 6 2 5 lo ca l p 0 (G a u s. σ ) 0 .5 5 (- 0 .1 4 ) 0 .2 1 (0 .8 ) 0 .6 5 (- 0 .4 ) 0 .9 (- 1 .3 ) 0 .6 (- 0 .2 6 ) 0 .8 5 (- 1 ) P ro ce ss S ig n a l R eg io n S R A ti g h t S R B ti g h t S R C ti g h t S R D ti g h t S R E ti g h t tt¯ + S in g le T o p 0 .2 2 ± 0 .3 5 (0 .0 4 6 ) 0 .2 1 ± 0 .3 3 (0 .0 6 6 ) 1 .8 ± 1 .6 (0 .9 6 ) 2 ± 1 .7 (0 .9 2 ) 3 .9 ± 4 (2 .6 ) Z / γ + je ts 2 .9 ± 1 .5 (3 .1 ) 2 .5 ± 1 .4 (1 .6 ) 2 .1 ± 1 .1 (4 .4 ) 0 .9 5 ± 0 .5 8 (2 .7 ) 3 .2 ± 1 .4 (1 .8 ) W + je ts 2 .1 ± 0 .9 9 (1 .9 ) 0 .9 7 ± 0 .6 (0 .8 4 ) 1 .2 ± 1 .2 (2 .7 ) 1 .7 ± 1 .5 (2 .5 ) 2 .3 ± 1 .7 (1 .5 ) Q C D je ts 7 .6 e − 0 9 ± 0 .0 0 2 4 (0 .0 0 2 ) 1 .4 e − 0 8 ± 0 .0 0 3 4 (0 .0 0 3 2 ) 5 .1 e − 0 9 ± 0 .0 0 5 8 (0 .0 0 2 3 ) 4 .4 e − 0 8 ± 0 .0 0 7 2 (0 .0 2 1 ) 0 .2 2 ± 0 .2 5 (0 .2 4 ) D i- B o so n s 1 .7 ± 0 .9 5 (2 ) 1 .7 ± 0 .9 5 (1 .9 ) 0 .4 9 ± 0 .2 6 (0 .5 1 ) 2 .2 ± 1 .2 (2 .2 ) 2 .5 ± 1 .3 (2 .5 ) T o ta l 7 ± 0 .9 9 9 (s y s) ± 2 .2 6 (s ta t) 5 .3 9 ± 0 .9 5 1 (s y s) ± 2 .0 1 (s ta t) 5 .6 8 ± 1 .7 9 (s y s) ± 1 .5 1 (s ta t) 6 .8 4 ± 1 .7 (s y s) ± 2 .1 (s ta t) 1 2 .1 ± 4 .5 9 (s y s) ± 3 .0 4 (s ta t) D a ta 1 1 1 4 9 1 3 lo ca l p 0 (G a u s. σ ) 0 .9 8 2 (- 2 .1 ) 0 .9 5 5 (- 1 .6 9 ) 0 .0 1 8 3 (2 .0 9 ) 0 .2 9 2 (0 .5 4 8 ) 0 .4 4 7 (0 .1 3 3 ) T ab le 5. 25 .: M o ri o n d ’1 2 n u m be rs o f ev en ts in d a ta a n d fi tt ed ba ck gr o u n d co m po n en ts in ea ch S R . T h e es ti m a te d ba ck gr o u n d va lu es a re qu o te d in th e o rd er “ ex pe ct a ti o n ± to ta l u n ce rt . (p re -fi t p re d ic ti o n )” . F o r th e to ta l ba ck gr o u n d es ti m a te s, th e tw o qu o te d u n ce rt a in ti es a re re sp ec ti ve ly sy st em a ti c a n d st a ti st ic a l (M C a n d C R st a ts co m bi n ed ). T h e va lu es in pa re n th es es a re th e p re -fi t p re d ic ti o n s, n o rm a li se d to cr o ss -s ec ti o n a n d lu m in o si ty . F o r W + je ts , Z + je ts a n d tt¯ + je ts , th es e p re d ic ti o n s a re fr o m A L P G E N sc a le d by fa ct o rs ex p la in ed el se w h er e in th e te xt . In th e ca se o f Q C D , th e p re -fi t va lu es a re fr o m th e d a ta -d ri ve n es ti m a te . F ro m [6 3 ]. 154 Experimental Studies P ro cess P ercen ta g es (% ) S R C lo ose S R E lo o se S R A m ed iu m S R A p m ed iu m S R C m ed iu m S R E m ed iu m tt¯+ sin g le t 3 5 (37) 56 (5 9 ) 1 1 (7.5 ) 9.5 (8.0) 31 (26) 49 (51) Z / γ + je ts 3 3 (3 0 ) 1 9 (1 2 ) 4 8 (5 0 ) 5 5 (5 5 ) 4 4 (4 1 ) 2 3 (1 7 ) W + jets 2 9 (30) 19 (2 1 ) 2 9 (3 1 ) 2 2 (24) 21 (28) 17 (8) Q C D jets 0 .18 (0.07 8) 3 .1 (3.5 ) 0 .2 2 (0.1 9 ) 8 .6× 1 0 − 7 (0 .30) 0.062 (0.034) 2.3 (2.5) D i-B oso n s 3 .7 (3.9 ) 3 .5 (3.9 ) 1 1 (1 1 ) 1 3 (13) 4.4 (4.4) 7.8 (11) P ro cess P ercen ta g es (% ) S R A tigh t S R B tig h t S R C tigh t S R D tigh t S R E tigh t tt¯+ sin g le t 3.2 (0.65) 3.9 (1.5 ) 3 2 (1 1) 29 (11) 32 (30) Z / γ + je ts 4 2 (4 4 ) 4 6 (3 6 ) 3 8 (5 1 ) 1 4 (3 2 ) 2 6 (2 1 ) W + jets 3 0 (27) 1 8 (1 9 ) 2 1 (3 1) 25 (31) 19 (17) Q C D jets 1 .1× 1 0 − 7 (0 .028) 2.6× 1 0 − 7 (0 .0 7 3 ) 9.1× 1 0 − 8 (0.027) 6 .4× 10 − 7 (0 .25) 1.8 (2.8) D i-B oson s 2 5 (28) 3 2 (4 3 ) 8.8 (5.9) 32 (26) 21 (29) T ab le 5.26.: M o rio n d ’1 2 percen ta ge co n tribu tio n s to th e S R ba ckgro u n d expecta tio n fro m T a ble 5 .2 5 fo r ea ch S M ba ckgro u n d co m po n en t. P a ren th eses in d ica te th e p re-fi t va lu es fro m M C . Experimental Studies 155 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRA (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (a) 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRA’ (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (b) 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 310 410 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRB (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (c) 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 310 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRC (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (d) 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRD (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (e) 0 500 1000 1500 2000 2500 3000 En trie s / 10 0 G eV 1 10 210 -1L dt = 4.7 fb∫ = 7 TeV)sData 2011 ( SM Total and single toptt W+jets Z+jets Diboson multijet SM+SU(500,570,0,10) SM+SU(2500,270,0,10) PreliminaryATLAS SRE (incl.) [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / S M 0 0.5 1 1.5 2 2.5 (f) Figure 5.18.: Moriond’12 meff(incl.) distributions in data and MC (ALPGEN) for all the 0` SRs prior to the meff(incl.) cut (red arrows indicate the start of a SR). The W + jets, Z + jets, tt¯ and single top contributions have additional scaled factors applied (explained elsewhere in the text). The multi-jet (QCD) contribution is as estimated using the corresponding data-driven method. The dashed-line histograms represent two mSUGRA/CMSSM benchmark model points (m0 = 500 GeV, m1/2 = 570 GeV, A0 = 0, tanβ = 10 and µ > 0 and with m0 = 2500 GeV, m1/2 = 270 GeV, A0 = 0, tanβ = 10 and µ > 0), which lie just beyond the reach of EPS’11. The yellow band represents the combined JES, JER and MC statistics uncertainties. 156 Experimental Studies 5.6.2. Discussion: Comparisons with other CRs To understand the relevance of CR1a in the 0` analysis, as well as its advantages over other control samples that could be used to estimate the same background, e.g. Z`` and W`ν , a few of comparisons will be made here between CR1a and other CRs, in particular those involving electroweak boson processes, i.e. CR1b (Z``) and CR3 (W`ν). The main topics will be the statistics, purity and uncertainties. CR statistics In Section 3.3, the theoretical advantages of the γ + jets sample to estimate the Z + jets background over other possibilities like Z`` + jets and W`ν + jets were discussed. Now the focus is on the experimental evidence supporting such arguments. When examining Table 5.22, the contrast between the available statistics in CR1a and CR1b is starkly evident. This is underlined by the fact that CR1b is the only CR to actually register zero events in data (for the 6-jet channel E), making it effectively unusable (e.g. it is disregarded in the 0` likelihood fit for this channel). Maintaining substantial CR statistics is of course critical for providing a robust SR estimate, since the CR statistical uncertainties feed directly into the SR prediction. The comparison with CR3 does not show such drastic differences, and the statistical advantage varies depending on the channel and meff(incl.) cut. But it is worth bearing in mind that some cuts (∆φ and EmissT /meff in Table 5.21) are relaxed in the case of the CR3 selection, whereas they are not in CR1a. While the omission of these cuts is not expected to substantially bias the SR predictions, full consistency would favour retaining them. Magnitude and stability of TFs A related issue arises from the magnitude of the TFs. From Table 5.23, it can be seen that the only TFs that are larger than 1 are those from CR1b. This feature results from the small branching fraction for Z`` decays. While at first glance this would not appear to present a problem, one may infer that the CR statistics will always be inferior to the number of events predicted in the SR. Therefore, the CR statistical uncertainty on the estimate will always be intrinsically larger than the Poisson uncertainty on the estimate itself – an undesirable state of affairs. Experimental Studies 157 In contrast, the CR1a TF values are without exception smaller than 0.5, and are in fact much more stable across the SRs relative to other CRs. To illustrate this, Table 5.27 shows the range, mean and standard deviations for the TFs in Table 5.23, broken down by CR. The standard deviation of CR1a is the smallest relative to the mean, at 13%, while the remainder are all in excess of 50%. While a degree of variation is inevitable due to the different kinematic selections of the various 0` SRs, stability is beneficial in that it offers a straightforward sanity check: the feature reflects the RZ/γ(pT) plateau at high pT (Figure 3.1(b)), as well as the minimal effect of the 0` selections on the photon acceptance, efficiencies and purity (Section 5.4.3). CR / Process Range Mean Std. Dev. CR1a / Z/γ+jets 0.130 0.319 0.042 CR1b / Z/γ+jets 4.700 3.46 1.545 CR2 / QCD jets 0.097 0.0254 0.029 CR3 / W+jets 0.600 0.296 0.167 CR4 / tt¯+ t 0.835 0.305 0.249 Table 5.27.: Moriond’12 range (difference between minimum and maximum values), mean and standard deviation of the TFs in Table 5.23, separated by CR/process. Purity A rough estimate of the purity of the various CR selections can be obtained by examining the corresponding meff(incl.) histogram, e.g. Figure 5.17, where the fraction of background at 1 TeV can be seen to be approximately 5% for CR1a and 3% for CR1b, but it is as large as 10% for CR3. Although the contamination can be compensated by an adequate knowledge of the contaminating processes, a purer sample benefits from reduced uncertainties, and is on the whole preferable. Uncertainties As an example, Table 5.28 shows the central values of the TFs for all CRs and the absolute values of their associated uncertainties, for the SR A (medium) (the complete collection can be found in[63]). Therefore, column 2 in this table is comparable to column 6 in Table 5.20 with the following caveats: 158 Experimental Studies • The “acc. Z+jets/γ” uncertainty represents a combined uncertainty by adding in quadrature the uncertainties in rows 2-4 and 7-8 in Table 5.20 (for simplicity, all these uncertainties are assumed uncorrelated with each other). • The uncertainties not filled for CR1a are only relevant to other CRs, e.g. the b-tag/veto efficiency, and therefore are not assessed. • The central value quoted in Table 5.28 has the RZ/Zνν scaling factor applied, as described in Section 5.6.1. • The “MET CellOut” uncertainty in Table 5.20 appears resolved into its components “cluster” and “pileup” in Table 5.28. For complementary purposes, Table 5.29 shows the influence of the various CRs uncertainties on the total SM background estimate for each SR. From these numbers, two important details can be noted. Firstly, the degree of correlation between the CR1a uncertainties and those of other CRs is really minimal – those systematics that are correlated (JER, JES, MET CellOut) are essentially negligible, when compared to the remaining uncorrelated systematics unique to CR1a. Secondly, the contribution of CR1a to the total uncertainty budget for the 0` SRs is rather substantial, except where MC or CR statistical uncertainties dominate. This is true at lower jet multiplicities and for softer meff(incl.) cuts. Essentially, this is due to Zνν + jets being the dominant background in these SRs, and does not reflect an innate weakness in the estimation method. However, it is clear that reducing the size of the uncertainties associated with CR1a can bring substantial gains in the performance of the 0` analysis as a whole (Section 5.6.3). As the dominant uncertainties can be traced to the lack of Zνν MC statistics used to compute RZ/γ, this problem is not insoluble, but merely underlines again the need for more appropriate MC samples. The theoretical studies from Chapter 4 and [64] indicate that it should be possible to decrease this uncertainty from 25% to about 10% under ideal circumstances, e.g. where multiparton MEs are used for all selected jets. Experimental Studies 159 R eg io n M a in C R / P ro ce ss C R 1 a / Z / γ + je ts C R 2 / Q C D je ts C R 4 / tt¯ + S in g le T o p C R 3 / W + je ts C R 1 b / Z / γ + je ts C en tr al va lu e 0. 39 0 .0 3 6 0 .3 5 0 .3 1 2 .5 J E R 0 .0 0 3 2 0 0 .0 9 2 0 − 0 .0 2 1 0 − 0 .1 4 0 J E S 0 .0 0 5 2 − 0 .0 0 3 7 − 0 .0 0 6 8 0 .0 2 7 0 .0 0 6 9 0 .0 1 7 − 0 .4 6 0 .9 P il eu p 0 0 .0 3 6 0 − 0 .0 1 4 l re so ln . − 0 .0 0 4 3 0 .0 0 9 4 − 0 .0 0 3 9 0 .0 0 2 7 0 − 0 T ri gg er − 0 .0 0 1 9 0 .0 0 1 9 − 0 .0 0 1 7 0 .0 0 1 7 − 0 .0 2 8 0 .0 2 9 b -t ag /v et o eff . − 0 .0 2 7 0 .0 4 − 0 .0 0 3 2 0 .0 0 3 2 ac c. Z + je ts / γ 0 .1 1 − 0 .1 1 l sc al e. − 0 .0 0 4 3 0 .0 0 5 7 − 0 .0 0 5 2 0 .0 0 0 4 7 − 0 .0 5 − 0 .0 3 4 Q C D sm ea r. 0 .0 3 1 − 0 .0 3 1 M E T C el lO u t cl u st er 0 .0 0 1 − 0 .0 0 0 7 2 0 .0 0 1 5 0 .0 0 0 6 5 − 0 .0 0 0 8 2 − 0 .0 0 1 5 T op T h eo ry 0 .2 1 − 0 .2 1 l eff . − 0 .0 0 2 4 0 .0 0 2 4 − 0 .0 0 2 0 .0 0 2 − 0 .0 3 2 0 .0 3 2 M E T C el lO u t p il eu p 0 .0 0 0 2 9 − 0 .0 0 0 7 9 − 0 .0 0 0 1 8 0 .0 0 7 8 − 0 .0 0 0 7 7 9 .4 e − 0 5 P D F 0 .0 0 6 1 − 0 .0 0 9 7 − 0 .0 0 6 7 0 .0 1 4 Z + je ts T h eo ry 0 .1 − 0 .1 M C st at . 0 .1 2 − 0 .1 2 0 .0 3 5 − 0 .0 3 5 0 .4 6 − 0 .4 6 W + je ts T h eo ry 0 .0 2 5 − 0 .0 2 5 T ab le 5. 28 .: M o ri o n d ’1 2 in it ia l (p re -fi t) u n ce rt a in ti es o n th e C R s T F s to S R A (m ed iu m ). F ro m [1 0 0 ]. 160 Experimental Studies U n certa in ty S ig n a l R eg io n S R A m ed iu m S R A tig h t S R A p m ed iu m S R B tig h t S R C lo o se S R C m ed iu m S R C tig h t S R D tig h t S R E lo o se S R E m ed iu m S R E tig h t T o ta l 1 2 2 .2 2 1 2 .1 2 8 8 2 .3 2 .7 4 0 7 5 .7 C R sta t / % 1 2 2 7 6 .8 2 4 9 .5 1 5 1 7 1 2 3 .9 2 3 7 M C sta t / % 1 6 6 2 1 0 6 2 1 2 2 0 2 6 3 6 4 .5 3 9 1 8 l reso ln . / % 0 .0 5 4 2 .6 0 .0 4 3 0 0 .0 7 6 0 .0 8 0 .0 1 0 0 .0 6 3 0 .2 0 .0 0 4 7 a cc. Z + jets/ γ / % 5 4 1 4 8 1 1 1 5 9 4 0 7 .6 0 .9 9 2 .1 9 .5 2 .1 M E T C ellO u t clu ster / % 0 .0 1 3 2 .7 0 .0 5 5 0 0 .3 2 0 .0 1 7 1 .8 1 .9 0 .0 7 7 0 .1 6 0 .1 4 M E T C ellO u t p ileu p / % 0 .0 0 5 6 0 0 .0 1 1 0 0 .1 5 0 .1 7 0 .0 0 2 6 0 0 .0 2 2 0 .2 5 0 T o p T h eo ry / % 1 2 2 .7 1 .2 0 5 .9 1 7 2 3 1 3 6 .6 1 5 1 9 P D F / % 0 .0 2 4 0 .1 5 0 .0 6 0 0 .1 9 0 .3 2 0 .0 1 9 0 0 .3 3 1 .4 0 B T a g W jets / % 0 .1 1 2 .7 0 .0 7 9 0 0 .7 1 0 .2 8 0 .0 1 4 0 0 .1 3 1 .2 0 .0 3 3 W + jets T h eo ry / % 1 .6 0 .6 5 0 .8 8 2 2 .8 5 8 .7 0 .8 1 0 .4 1 .2 0 .2 2 l sca le. / % 0 .0 9 7 2 .6 0 .0 2 2 0 0 .1 3 0 .1 2 0 .0 0 7 1 0 0 .0 8 0 .2 1 0 G en eric D ib o so n / % 3 .9 1 1 5 .7 1 2 0 .0 1 6 0 .1 6 0 .0 1 7 1 4 0 .0 5 2 1 .8 4 .4 l eff . / % 0 .0 1 2 2 .7 0 .0 5 3 0 0 .1 6 0 .1 3 0 .0 1 2 0 0 .0 3 0 .1 8 0 J E S / % 0 2 .7 0 .2 3 0 .6 1 0 .5 3 0 .0 8 0 .8 0 4 5 1 .3 3 2 P ileu p / % 0 2 .6 0 .0 2 3 0 .0 4 9 0 .3 9 0 .6 3 0 .0 0 9 3 1 .4 0 .1 0 .1 4 0 .0 0 7 T rig g er / % 0 .0 1 5 1 .8 0 .0 1 1 0 0 .1 0 .1 3 0 .0 0 3 1 0 0 .0 2 3 0 .1 7 0 J E R / % 0 1 .5 0 2 .1 0 .9 3 3 .4 1 3 1 7 0 .8 9 0 .8 1 6 .4 B T a g to p / % 1 .1 2 .7 0 .4 9 0 9 .2 3 .3 3 .1 4 5 .1 7 .4 1 .3 Q C D sm ea r. / % 0 .0 1 8 1 .7 0 .0 0 1 6 0 0 .0 5 6 0 .1 3 0 .0 0 1 1 0 0 .2 0 .4 5 0 .0 1 4 T ab le 5.29.: M o rio n d ’1 2 brea kd o w n o f th e in fl u en ce o f va rio u s system a tic u n certa in ties in th e S R s. T h e “ T o ta l” ro w sh o w s th e a bso lu te u n certa in ty o n th e S R p red ictio n . A ll o th er ro w s sh o w th e fra ctio n a l co n tribu tio n o f in d ivid u a l system a tics to th is n u m ber, a s fo llo w s: ‘C R sta t’ is th e u n certa in ty w ith a ll u n certa in ties besid es th e sta tistica l u n certa in ty in th e C R sw itch ed o ff , ‘M C sta t’ is th e u n certa in ty co m in g fro m lim ited M C sa m p le sizes; a ll o th er en tries sh o w th e in fl u en ce o f th e co rrespo n d in g system a tic u n certa in ty. ‘M C sta t’ u n certa in ties a re m od elled w ith a log n o rm a l pd f sh a pe, w h ile ‘C R sta t’ u n certa in ties a re ba sed o n P o isso n pd fs. N o te: T h e in fl u en ce o f M C sta t. a n d a ll system a tic u n certa in ties a G a u ssia n sh a pe fo r a ll u n d erlyin g p ro b. d en sity fu n ctio n s. F ro m [1 0 0 ]. Experimental Studies 161 5.6.3. 0` Interpretation and Limits In the absence of a statistically significant excess, limits are set on contributions to the SRs from new physics, which has been the case in all the 0` analyses to date. For the purposes of interpretation, a SR measurement is compared with the corre- sponding background estimate in order to determine the significance of any excesses over the SM expectation, or to test its compatibility with respect to a given signal model10. In other words, a hypothesis test is carried out. The so-called discovery test regards the SM prediction as the “null” hypothesis, i.e. the model to be falsified if the observation is substantially incompatible with it, like an excess. Alternatively, one can test the compatibility of particular BSM model with the observation in order to exclude incompatible models. Therefore, exclusion tests become of interest when no significant excesses are observed. The ATLAS SUSY Working Group policy has been so far to present both discovery and exclusion results in all cases. In the 0` fitting procedure, any of these hypothesis tests can be performed by just assuming the appropriate signal component in the likelihood function (Equation (5.12)). When searching for an excess it is assumed that the SUSY signal contributes minimally to the CR counts. For the purposes of a discovery test, the CRs are simply treated as signal-free, since no particular signal is assumed. However, it is possible to account for the signal contamination in CRs, and this is indeed done when carrying out an exclusion test on some specific model. Since no significant excess has been observed until now, in the 0` analysis the focus has been on setting exclusion limits whilst still providing the the p-values for the discovery test, as shown in Table 5.25. For the interpretation to be as generic as possible, model- independent limits have been set on the SUSY cross-section times acceptance times efficiency, σSUSY · A · ε, i.e. remaining agnostic about the model kinematics and detector effects. The limits set on σSUSY · A · ε are listed in Table 5.30. Such numerical values can be reinterpreted easily by computing σSUSY ·A · ε for a given signal model and comparing this with the ATLAS limits. The limits on a specific SUSY model are obtained by comparing the observed numbers of events in the SR (s) with the fitted SM background expectation plus SUSY signal process (s+ b), using the CLs method [24] to derive 95% Confidence Level (CL) exclusion regions. The SR with the best expected limit at each point in the SUSY parameter space is chosen as the combined limit. These procedures 10In principle, deficits could also mark new physics destructively interfering with SM particle production, but this is not considered here. 162 Experimental Studies follow the ATLAS Statistics Forum recommendations and are explained in more detail in [100] and [104]. The two main interpretations of the results in the Moriond’12 0` analysis are presented in Figure 5.19. Figure 5.19(a) represents an exclusion region in the MSSM squark-gluino mass plane for a set of simplified SUSY models (see Section 1.2.2) with mχ˜01 = 0 and degenerate gluino and squark masses of the first two generations. All other supersymmetric particles, including the squarks of the third generation, are decoupled by being given masses of 5 TeV. From this, the limit on the gluino mass is approximately mg˜ ∼ 940 GeV, and on the squark mass mq˜ ∼ 1380 GeV. As for Figure 5.19(b), it represents an interpretation in an MSUGRA constrained model (see Section 1.2.2) with parameters tan β = 10, A0 = 0, µ > 0. From this, the limit on m1/2 is above 300 GeV at high m0 and reaches 680 GeV for low values of m0 – the inclusion of SRs with larger jet multiplicities improved the reach at large m0. Equal mass squarks and gluinos are excluded below 1400 GeV in both scenarios. Overall, the increased data sample in the Moriond’12 analysis allowed for the substantial extension of the limits from EPS’11. Signal Region SRC loose SRE loose SRA medium SRAp medium SRC medium SRE medium Limit (fb) 12(13+9.3−18 ) 18(15 +11 −20) 5.3(6 +4.3 −8.2) 6.2(9.2 +6.7 −13 ) 3.7(4.1 +3 −5.7) 2.5(3.5 +2.5 −5 ) Signal Region SRA tight SRB tight SRC tight SRD tight SRE tight Limit (fb) 0.62(1.3+0.89−1.9 ) 0.65(1.2 +0.8 −1.8) 3.5(2.3 +1.6 −3.2) 2.2(1.9 +1.4 −2.7) 2.6(2.5 +1.8 −3.5) Table 5.30.: Moriond’12 Approximate observed limits on the model independent cross section at 95 % C.L. based on the CLs method, no signal uncertainties are taken into account. The expected cross section is given in brackets with a ±1σ deviation in the background. Experimental Studies 163 gluino mass [GeV] 600 800 1000 1200 1400 1600 1800 2000 sq ua rk m as s [G eV ] 600 800 1000 1200 1400 1600 1800 2000 = 100 fbSUSYσ = 10 fbSUSYσ = 1 fbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 4.71 fb∫ Combined PreliminaryATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit ATLAS EPS 2011 [GeV]0m 500 1000 1500 2000 2500 3000 3500 4000 [G eV ] 1/ 2 m 200 300 400 500 600 700 (600)g~ (800)g~ (1000)g~ (1200)g~ (600) q~ (1000) q ~ (1400) q ~ (1800) q ~ >0µ= 0, 0 = 10, AβMSUGRA/CMSSM: tan =7 TeVs, -1 L dt = 4.71 fb∫ Combined PreliminaryATLAS observed 95% C.L. limitsCL median expected limitsCL ATLAS EPS 2011 LSPτ∼ LEP Chargino No EWSB Figure 5.19.: Moriond’12 95% CLs exclusion limits obtained in the 0` analysis by using the SR with the best expected sensitivity at each point in (a) a simplified MSSM scenario with only strong production of gluinos and first- and second-generation squarks, and direct decays to jets and neutralinos; and (b) in the (m0 ; m1/2) plane of MSUGRA/CMSSM for tanβ = 10, A0 = 0 and µ > 0. The red lines show the observed limits, the dashed-blue lines the median expected limits, and the dotted blue lines the ±1σ variation on the expected limits. The EPS’11 and LEP limits are also shown. From [58]. Effects of CR1a Zνν + jets estimate The reduction of uncertainties in any background estimation method is a high priority. In particular, where a given background component is irreducible, and cannot be eradicated from the SR selection entirely, it is best to ensure that the magnitude of the component is known precisely. To illustrate the extent to which this is true, a comparison is made in Figure 5.20 of limits computed assuming a 25% theoretical uncertainty on the ratio RZ/γ (as was assumed for Moriond’12) with those assuming a 15% uncertainty. All other parameters were kept unchanged. Two SR selections, SR A (medium) and SR A’ (medium) are shown, as these are the ones for which the Z + jets background is most dominant (48% and 55%, see Table 5.26). The limits improve perceptibly when the uncertainty is reduced, by up to 40 GeV in the squark and gluino masses. 164 Experimental Studies gluino mass [GeV] 600 800 1000 1200 1400 1600 1800 2000 sq ua rk m as s [G eV ] 600 800 1000 1200 1400 1600 1800 2000 = 100 fbSUSYσ = 10 fbSUSYσ = 1 fbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 4.71 fb∫ > 1400 eff0 lepton 2012 SRA m InternalATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit ATLAS EPS 2011 (a) SR A, meff > 1.4 TeV, σth = 25% gluino mass [GeV] 600 800 1000 1200 1400 1600 1800 2000 sq ua rk m as s [G eV ] 600 800 1000 1200 1400 1600 1800 2000 = 100 fbSUSYσ = 10 fbSUSYσ = 1 fbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 4.71 fb∫ > 1200 eff0 lepton 2012 SRAp m InternalATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit ATLAS EPS 2011 (b) SR A’, meff > 1.2 TeV, σth = 25% gluino mass [GeV] 600 800 1000 1200 1400 1600 1800 2000 sq ua rk m as s [G eV ] 600 800 1000 1200 1400 1600 1800 2000 = 100 fbSUSYσ = 10 fbSUSYσ = 1 fbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 4.71 fb∫ > 1400 eff0 lepton 2012 SRA m InternalATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit ATLAS EPS 2011 (c) SR A, meff > 1.4 TeV, σth = 15% gluino mass [GeV] 600 800 1000 1200 1400 1600 1800 2000 sq ua rk m as s [G eV ] 600 800 1000 1200 1400 1600 1800 2000 = 100 fbSUSYσ = 10 fbSUSYσ = 1 fbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 4.71 fb∫ > 1200 eff0 lepton 2012 SRAp m InternalATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit ATLAS EPS 2011 (d) SR A’, meff > 1.2 TeV, σth = 15% Figure 5.20.: Moriond’12 comparison of limits set using the predicted CR1a Z+jets background estimate from Figure 5.16 with different systematic uncertainties. The red solid and blue dashed lines indicates the observed and expected 95% C.L. excluded regions, while the shaded orange region is the excluded area from EPS’11. The upper two plots show the nominal 25% theory uncertainty, σth, estimated for Moriond’12. In the lower plots, this magnitude of this uncertainty is reduced to 15%, resulting in a strengthening of the limits by up to 40 GeV in the squark and gluino masses, providing a strong motivation for improving the estimation of the CR1a TFs. The SRs shown are those that are dominated by the Zνν + jets background due to the less stringent jet multiplicity requirements. The ‘holes/loops’ shown reflect MC fluctuations or divergences encountered by the fit for those regions of phase space. Part III. Close 165 Chapter 6. Conclusions & Outlook 6.1. ZfromGamma In conclusion, the ZfromGamma method was demonstrated to be successful in estimating the Zνν background to new physics searches in ATLAS, as well as well-established since 2010. Despite no signs of SUSY or other BSM physics found so far at the LHC (see Section 6.2), the searches continue and therefore, the ZfromGamma method will remain crucial in determining if there are signs of new physics at all. However, there remains room for improvement: a further reduction in the uncertainties associated with this method would pay substantial dividends in improving the sensitivity and reach of the searches for new physics. In this section, some potential steps that might advance the precision and overall applicability of the method are outlined, but first, to understand some of the motivations behind these, a discussion of analogous CMS results precedes. 6.1.1. CMS results This part focuses on the “ZfromGamma-like” results from CMS. First, the most comparable studies in CMS to the ATLAS 0` analysis are their so-called “SUSY hadronic searches”. The analyses which have used a similar dataset to the Moriond’12 one discussed here are: (i) the “multijets+MHT” search (4.98 fb−1) [105]; (ii) the “MT2” search (4.73 fb−1) [106]; (iii) the “razor” search (4.4 fb−1) [107]; where (i) is the closest with respect to the 0` event selection. From these, (i) and (ii) have used a ZfromGamma-like method to estimate the Zνν + jets background as overviewed below. 167 168 Conclusions & Outlook MHT + jets: The baseline selection for this search was HT > 500 GeV, HT > 200 GeV, at least 3 jets with pT > 50 GeV and |η| < 2.5 and ∆φ(HT, j1) > 0.5, ∆φ(HT, j2) > 0.5 and ∆φ(HT, j3) > 0.3; where HT = ∑ pT(selected jets). Roughly speaking, HT is analogous to the 0` meff and HT to the 0` E miss T . As in the 0` search, Zνν + jets is usually either the largest or second-largest background to this search, as shown in Figure 6.1, so determining this background is also very important here. For this, a similar method to ZfromGamma is used and the plots analogous to CR1a are shown in Figure 6.2 as a function of HT and HT. Some systematic data/MC discrepancies can be noticed in Figure 6.2(a) at low HT (HT < 1 TeV), perhaps due to missing electroweak backgrounds in the MC, as well as in Figure 6.2(b) for medium HT (250 GeV <HT < 500 GeV). However, the overall data-driven prediction for the total SM background agrees well with the distributions in data (example plots can be found in [105]). <800T 5001400T H N um be r o f E ve nt s 1 10 210 310 410 < 35 0 TH 20 0< < 50 0 TH 35 0< < 60 0 TH 50 0< > 60 0 TH < 35 0 TH 20 0< < 50 0 TH 35 0< <6 00 TH 50 0< > 60 0 TH < 35 0 TH 20 0< < 50 0 TH 35 0< > 50 0 TH < 35 0 TH 20 0< > 35 0 TH > 20 0 TH Data +Jetsνν →Z )+Jetsν+hadrτ(tW/t )+Jetsν+µ(e/tW/t QCD Total uncertainty on measured background CMS Preliminary = 7 TeVs, -1L = 4.98 fb [GeV]TH [GeV]TH N um be r o f E ve nt s N um be r o f E ve nt s Figure 6.1.: CMS Moriond’12 “MHT+jets” search. Summary of number of events observed in data and prediction of various backgrounds from data in 14 “search bins” defined in bins of HT and HT (from [105]). Conclusions & Outlook 169 (a) (b) Figure 6.2.: CMS Moriond’12 “MHT+jets” search. Comparison of the γ + jets control sample in data and MC: (a) HT and (b) HT after all the baseline selection has been applied (from [105]). MT2 + jets: This search is based on a different discriminating variable to meff called mT2, which was in fact used once in the 0` analysis to define one of the Moriond’11 SRs (see Appendix C.1.4). As in the 0` analysis, two control samples are obtained to determine the Zνν + jets background; one of them being γ + jets and the other Wµν + jets. As in ZfromGamma, in both cases, Zνν is mimicked by removing, respectively, the γ and µ from the event, and adding the corresponding pT to the EmissT . In the case of γ+jets, the QCD contamination was estimated from MC in the CR (via a shower shape fit). The data to MC comparison of the mT2 distribution for the CR is shown in Figure 6.3. The Zνν background was estimated for each bin in mT2 from the number of prompt photon events multiplied by the RZ/γ(mT2) from MC. Despite being calculated as a function of mT2, the photon pT is what drives the mT2 value, i.e. RZ/γ(mT2(pT)) = RZ/γ(pT), and so the same features discussed for in previous chapters for RZ/γ(pT) apply. The background prediction was found to be in excellent agreement with the MC expectation. The main uncertainties in their estimate come from control sample statistics, the shower shape fit (5%) and RZ/γ. In particular, for RZ/γ , the uncertainty was obtained first comparing the photon pT spectra between MADGRAPH and JetPhox NLO generators, and then comparing the pT dependence of the ratio in MC to the one in data by using Z`` events (the latter being similar to the ZfromGamma “Zµµ cross-check”, see Appendix D.1), as shown in Figure 6.4(b). With these, the uncertainty obtained was < 20% for mT2 < 275 GeV and < 30% for mT2 > 275 GeV (the latter being larger due to the limited Z`` statistics for pT > 400 GeV). In the reference for this analysis [106], there is no mention of photon efficiencies nor acceptance corrections. 170 Conclusions & Outlook As for the alternative method which used Wµν , the main challenge was to estimate the relatively large tt¯ contamination in the control sample. However, both methods were found to be in good agreement and the weighted average of the two is taken as the final estimate (they are assumed statistically uncorrelated). The uncertainties on the Wµν are not quoted in the reference either. Another feature of this analysis is that the Zνν background is always comparable to the W`ν and top backgrounds in the SRs (as shown by the SRs plots in [106]). Figure 6.3.: CMS Moriond’12 “MT2” search. Photon mT2 spectrum in data and MC, where the photon was added to the EmissT -vector to mimic the Zνν kinematics. (from [106]). 6.1.2. Outlook It is possible to further improve the ZfromGamma method in a variety of ways. The following is a list with some ideas: • Overall, the aim would be to reduce each of the uncertainties associated with the method, to help maximise the BSM search reach (see Section 5.6.3). • Despite the very high purity of the CR1a sample, a proper estimation of the background contamination (fbkg) in the sample should be done (currently, the CMS MT2 search implements a method to do so, see Section 6.1.1). This could potentially Conclusions & Outlook 171 (a) (b) Figure 6.4.: CMS Moriond’12 “MT2” search. (a) Vector boson pT for Z(ee, µµ) and γ + jets events for data and MC. (b) Z(ee, µµ) to γ+ jets ratio as a function of vector boson transverse momenta both for data and MC. Only statistical errors are shown (both from [106]). reduce the uncertainty on fbkg. For the 0` analysis, this could also determine the cross-TFs to other CRs. • Obtain RZ/γ from data rather than from MC, as currently done in CMS (Fig- ure 6.4(b)), also aiming to reduce further the theoretical uncertainty, especially at low-pT, where the data statistics should not be so limited. • Evaluate the variation of RZ/γ with respect to other kinematic variables e.g. as a function of η, meff , Njets, HT, etc (as done by CMS for mT2, see Section 6.1.1), and determine the thresholds and conditions at which such effects can be safely ignored. • Determine RZ/γ at √ s = 8 TeV, given that this is the new c.o.m. energy at which the LHC will operate throughout 2012 and that the ratio is expected to slightly increase (see Figure 3.1(b)) • Investigate the effects on RZ/γ from electroweak corrections e.g. Sudakov logarithms (see Section 4.5), involving W/Z virtual exchanges. • Look at the possibility of determining from the RZ/γ dependence on αS, the renor- malisation scale Qren “chosen” by data e.g. from the ratio αS(Q 2 Z)/αS(Q 2 γ) as illustrated in Figure 4.9. 172 Conclusions & Outlook 6.2. SUSY and other BSM No evidence of SUSY at the LHC has been found up to now, meaning that no excess has been observed above expected backgrounds in the various searches. This has been interpreted as new limits on physically relevant quantities of many BSM models. Figure 6.5 shows a summary of the latest ATLAS SUSY reaches as of Moriond’12. The plot features the different search categories: “Inclusive searches”, “Third generation”, “Direct gaugino”, “Long-lived particles” and “RPV”, some of which are described below. The limits so far set by CMS on these models are very similar so they will not be discussed here, but an equivalent plot can be found in [108]. Mass scale [TeV] -110 1 10 R PV Lo ng -li ve d pa rti cle s D G Th ird g en er at io n In cl us iv e se ar ch es klm ≈ ijmHypercolour scalar gluons : 4 jets, ,missTEMSUGRA/CMSSM - BC1 RPV : 4-lepton + ,missTEBilinear RPV : 1-lep + j’s + µRPV : high-mass e τ∼GMSB : stable SMP : R-hadrons (Pixel det. only) SMP : R-hadrons SMP : R-hadrons Stable massive particles (SMP) : R-hadrons ± 1 χ∼AMSB : long-lived ,missTE) : 3-lep + 01χ ∼ 3l → 0 2 χ∼± 1 χ∼Direct gaugino ( ,missTE) : 2-lep SS + 01χ ∼ 3l → 0 2 χ∼± 1 χ∼Direct gaugino ( ,missT Ell) + b-jet + → (GMSB) : Z(t~t~Direct ,missTE) : 2 b-jets + 01χ ∼ b→1b ~ (b~b~Direct ,missTE) : multi-j’s + 01χ ∼tt→g~ (t~Gluino med. ,missTE) : 2-lep (SS) + j’s + 01χ ∼tt→g~ (t~Gluino med. ,missTE) : 1-lep + b-j’s + 01χ ∼tt→g~ (t~Gluino med. ,missTE) : 0-lep + b-j’s + 01χ ∼bb→g~ (b~Gluino med. ,missT E + γγGGM : ,missT E + j’s + τGMSB : 2- ,missT E + j’s + τGMSB : 1- ,missTE + SFGMSB : 2-lep OS ,missTE) : 1-lep + j’s + ±χ∼q q→g~ (±χ∼Gluino med. ,missTEPheno model : 0-lep + j’s + ,missTEPheno model : 0-lep + j’s + ,missTEMSUGRA/CMSSM : multijets + ,missTEMSUGRA/CMSSM : 1-lep + j’s + ,missTEMSUGRA/CMSSM : 0-lep + j’s + 3 GeV)± 140 ≈ sgm < 100 GeV, sgmsgluon mass (excl: 185 GeV (2010) [1110.2693]-1=34 pbL massg~1.77 TeV (2011) [ATLAS-CONF-2012-035]-1=2.1 fbL < 15 mm)LSPτ mass (cg~ = q~760 GeV (2011) [1109.6606]-1=1.0 fbL =0.05)312λ=0.10, , 311λ mass (τν∼1.32 TeV (2011) [1109.3089]-1=1.1 fbL massτ∼136 GeV (2010) [1106.4495]-1=37 pbL massg~810 GeV (2011) [ATLAS-CONF-2012-022]-1=2.1 fbL masst~309 GeV (2010) [1103.1984]-1=34 pbL massb~294 GeV (2010) [1103.1984]-1=34 pbL massg~562 GeV (2010) [1103.1984]-1=34 pbL ) < 2 ns, 90 GeV limit in [0.2,90] ns)±1χ ∼(τ mass (1 < ±1χ ∼118 GeV (2011) [CF-2012-034]-1=4.7 fbL ) < 170 GeV, and as above)01χ ∼(m mass (±1χ ∼250 GeV (2011) [ATLAS-CONF-2012-023]-1=2.1 fbL )))02χ ∼(m) + 01χ ∼(m(2 1) = ν∼,l~(m), 02χ ∼(m) = ±1χ ∼(m, 01χ ∼) < 40 GeV, 01χ ∼(m mass ((±1χ ∼ 170 GeV (2011) [1110.6189]-1=1.0 fbL ) < 230 GeV)01χ ∼(m mass (115 < t~310 GeV (2011) [ATLAS-CONF-2012-036]-1=2.1 fbL ) < 60 GeV)01χ ∼(m mass (b~390 GeV (2011) [1112.3832]-1=2.1 fbL ) < 200 GeV)01χ ∼(m mass (g~830 GeV (2011) [ATLAS-CONF-2012-037]-1=4.7 fbL ) < 210 GeV)01χ ∼(m mass (g~650 GeV (2011) [ATLAS-CONF-2012-004]-1=2.1 fbL ) < 150 GeV)01χ ∼(m mass (g~710 GeV (2011) [ATLAS-CONF-2012-003]-1=2.1 fbL ) < 300 GeV)01χ ∼(m mass (g~900 GeV (2011) [ATLAS-CONF-2012-003]-1=2.1 fbL ) > 50 GeV)01χ ∼(m mass (g~805 GeV (2011) [1111.4116]-1=1.1 fbL > 20)β mass (tang~990 GeV (2011) [ATLAS-CONF-2012-002]-1=2.1 fbL > 20)β mass (tang~920 GeV (2011) [ATLAS-CONF-2012-005]-1=2.1 fbL < 35)β mass (tang~810 GeV (2011) [ATLAS-CONF-2011-156]-1=1.0 fbL ))g~(m)+0χ∼(m(2 1) = ±χ∼(m) < 200 GeV, 01χ ∼(m mass (g~900 GeV (2011) [ATLAS-CONF-2012-041]-1=4.7 fbL )01χ ∼) < 2 TeV, light q~(m mass (g~940 GeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL )01χ ∼) < 2 TeV, light g~(m mass (q~1.38 TeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL )0m mass (large g~850 GeV (2011) [ATLAS-CONF-2012-037]-1=4.7 fbL massg~ = q~1.20 TeV (2011) [ATLAS-CONF-2012-041]-1=4.7 fbL massg~ = q~1.40 TeV (2011) [ATLAS-CONF-2012-033]-1=4.7 fbL Only a selection of the available mass limits on new states or phenomena shown* -1 = (0.03 - 4.7) fbLdt∫ = 7 TeVs ATLAS Preliminary ATLAS SUSY Searches* - 95% CL Lower Limits (Status: March 2012) Figure 6.5.: Mass reach of ATLAS searches for Supersymmetry. Only a representative selection of the available results is shown. The format of each row is “Model name: signature — Luminosity (data sample), [reference] — 95% CL mass exclusion — Observable”. Status of figure: Moriond’12 (from [13]). Conclusions & Outlook 173 RPC searches: The 0` search currently sets the most stringent limits on squark and gluino masses in the constrained and simplified models discussed in Section 5.6.3. For GMSB models, the 2`+jets excludes SUSY-breaking scales of Λ ∼ 40 TeV[109], but the most stringent limits are set by the γγ search on the SPS8 breaking-scale up to Λ ∼ 145 TeV and other GMSB models (GGM) [110]. For AMSB models, a search for a long-lived χ˜ ± 1 decaying inside the ATLAS detector to χ˜ 0 1 + pi± resulting in final-states of EmissT + 0l + jets and a disappearing track sets limits on the χ˜ ± 1 lifetime between 0.5-2 ns. The 2` + jets search is able to constrain the masses of charginos up to 200 GeV. The specialised searches for third generation squarks (“b-jet searches”) set the most stringent limits on stops and sbottoms in simplified models where the third generation is assumed to be the lightest, while first and second are decoupled from the theory. The highlight of the 0`+ b-jet search is to exclude sbottom masses up to 390 GeV [111], while in 1`+ b-jet search is to exclude stop masses up to 300 GeV [112]. RPV: In ATLAS these are less popular than the RPC searches, so fewer results are available. Starting with the long-lived particle searches, the 1` + jets search has also an interpretation in a bilinear RPV (bRPV) mSUGRA model [113], where equal squark and gluino masses below 760 GeV are excluded [113]. A search for a long-lived χ˜ 0 1 which decays to high-pT µ+jets leaving a displaced vertex has set limits on a SUGRA model, excluding 150 GeV squarks for any single displaced vertex. There have been also other searches looking for “resonance” signatures, such as the ν˜τ → eµ search and the scalar gluon search (g˜ → jets). Despite no signs of SUSY so far, the searches for it will continue at the LHC this year and with a higher c.o.m. (8 TeV). As discussed in Section 1.2.2, the SUSY parameter space is enormous and many models still remain to be explored. On the other hand, the present experimental limits on SUSY are now strong enough to re-evaluate whether SUSY can still address the problems it aims to solve, which is why alternative BSM theories are simultaneously searched for in ATLAS. Other BSM There are many other theories similarly motivated by the improvements they could offer to the SM problems. Given that no sign of SUSY has been observed so far (Section 1.2.3), it is becoming even more appealing now to pursue these alternatives, which in ATLAS 174 Conclusions & Outlook are referred altogether as “Exotics”. Figure 6.6 shows a summary of the latest ATLAS Exotics reaches as of Moriond’12, where they have been arranged into six categories: extra dimensions (ED), contact interactions (CI), exotic vector bosons (V ′), leptoquarks (LQ), fourth-generation (4th gen.) and ‘other’, which includes less popular searches (technicolor, Majorana neutrinos, excited quarks, axigluons, etc). However, even in all these many different searches, no new physics signs have showed up either. However, the plan is also to continue these analyses in 2012, as well as other new alternatives. In conclusion, despite the main outcome from the LHC so far could be seen as only “disproving theories”, the reader should not be discouraged – the LHC is a long term experiment and the next few years are really going to show which theories are actually correct. Mass scale [TeV] -110 1 10 210 O th er Ex ci t. fe rm . N ew q ua rk s LQ V’ CI Ex tra d im en sio ns llqmVector-like quark : NC, qνlmVector-like quark : CC, jjmColor octet scalar : dijet resonance, µµm)=1) : SS dimuon, µµ→L ±± (DY prod., BR(HL±±H (LRSM, no mixing) : 2-lep + jetsRW Major. neutr. (LRSM, no mixing) : 2-lep + jets,WZT mlll), νTechni-hadrons : WZ resonance ( µµee/ mTechni-hadrons : dilepton, γµm resonance, γ-µExcited muon : γem resonance, γExcited electron : e- jjmExcited quarks : dijet resonance, jetγm-jet resonance, γExcited quarks : ,missTE : 1-lep + jets + 0A0 + At t→ exo. 4th gen.TT Zb m Zb+X, →’bNew quark b’ : b’ WtWt→4d4 generation : d th4 WbWb→4u4 generation : u th4 WqWq→4Q4 generation : Q th4 jjνµjj, µµ=1) : kin. vars. in βScalar LQ pairs ( jjν=1) : kin. vars. in eejj, eβScalar LQ pairs ( µT,e/mSSM W’ : µµee/mSSM Z’ : ,missTEuutt CI : SS dilepton + jets + ll m combined, µµqqll CI : ee, )jjm(χqqqq contact interaction : )jjm(χQuantum black hole : dijet, F T pΣ=3) : leptons + jets, DM /THMADD BH ( ch. part.N=3) : SS dimuon, DM /THMADD BH ( jetsN, TpΣ=3) : multijet, DM /THMADD BH ( tt m l+jets, → t=-0.20 : t s g/ qqgKK gRS with llll / lljjm = 0.1 : ZZ resonance, PlM/kRS with llm = 0.1 : dilepton, PlM/kRS with γγm = 0.1 : diphoton, PlM/kRS with ,missT E + γγUED : Large ED (ADD) : diphoton Large ED (ADD) : monojet )Q/mν = qQκQ mass (coupling 760 GeV (2011) [1112.5755]-1=1.0 fbL )Q/mν = qQκQ mass (coupling 900 GeV (2011) [1112.5755]-1=1.0 fbL Scalar resonance mass1.94 TeV (2011) [ATLAS-CONF-2012-038]-1=4.8 fbL massL ±±H355 GeV (2011) [1201.1091]-1=1.6 fbL (N) < 1.4 GeV)m mass (RW2.4 TeV (2011) [Preliminary]-1=2.1 fbL ) = 2 TeV)R(WmN mass (1.5 TeV (2011) [Preliminary]-1=2.1 fbL )) T ρ(m) = 1.1 T(am, Wm) + Tpi(m) = Tρ(m mass (Tρ483 GeV (2011) [Preliminary]-1=1.0 fbL ) = 100 GeV)Tpi(m) - Tω/Tρ(m mass (Tω/Tρ470 GeV (2011) [ATLAS-CONF-2011-125]-1=1.1-1.2 fbL *))µ = m(Λ* mass (µ1.9 TeV (2011) [ATLAS-CONF-2012-023]-1=4.8 fbL = m(e*))Λe* mass (2.0 TeV (2011) [ATLAS-CONF-2012-023]-1=4.9 fbL q* mass3.35 TeV (2011) [ATLAS-CONF-2012-038]-1=4.8 fbL q* mass2.46 TeV (2011) [1112.3580]-1=2.1 fbL ) < 140 GeV)0(AmT mass (420 GeV (2011) [1109.4725]-1=1.0 fbL b’ mass400 GeV (2011) [Preliminary]-1=2.0 fbL mass4d480 GeV (2011) [Preliminary]-1=1.0 fbL mass4u404 GeV (2011) [1202.3076] -1 =1.0 fbL mass4Q350 GeV (2011) [1202.3389]-1=1.0 fbL gen. LQ massnd2685 GeV (2011) [Preliminary]-1=1.0 fbL gen. LQ massst1660 GeV (2011) [1112.4828]-1=1.0 fbL W’ mass2.15 TeV (2011) [1108.1316]-1=1.0 fbL Z’ mass2.21 TeV (2011) [ATLAS-CONF-2012-007]-1=4.9-5.0 fbL Λ1.7 TeV (2011) [1202.5520]-1=1.0 fbL (constructive int.)Λ10.2 TeV (2011) [1112.4462]-1=1.1-1.2 fbL Λ7.8 TeV (2011) [ATLAS-CONF-2012-038]-1=4.8 fbL =6)δ (DM4.11 TeV (2011) [ATLAS-CONF-2012-038]-1=4.7 fbL =6)δ (DM1.5 TeV (2011) [ATLAS-CONF-2011-147]-1=1.0 fbL =6)δ (DM1.25 TeV (2011) [1111.0080]-1=1.3 fbL =6)δ (DM1.37 TeV (2010) [ATLAS-CONF-2011-068]-1=35 pbL KK gluon mass1.03 TeV (2011) [ATLAS-CONF-2012-029]-1=2.1 fbL Graviton mass845 GeV (2011) [1203.0718]-1=1.0 fbL Graviton mass2.16 TeV (2011) [ATLAS-CONF-2012-007]-1=4.9-5.0 fbL Graviton mass1.85 TeV (2011) [1112.2194]-1=2.1 fbL Compact. scale 1/R (SPS8)1.23 TeV (2011) [1111.4116]-1=1.1 fbL (GRW cut-off)SM3.0 TeV (2011) [1112.2194]-1=2.1 fbL =2)δ (DM3.2 TeV (2011) [ATLAS-CONF-2011-096]-1=1.0 fbL Only a selection of the available mass limits on new states or phenomena shown* -1 = (0.04 - 5.0) fbLdt∫ = 7 TeVs ATLAS Preliminary ATLAS Exotics Searches* - 95% CL Lower Limits (Status: March 2012) Figure 6.6.: Mass reach of ATLAS searches for new phenomena other than SUSY. Only a representative selection of the available results is shown. The format of each row is “Model name: signature — Luminosity (data sample), [reference] — 95% CL mass exclusion — Observable”. Status of figure: Moriond’12 (from [13]). Conclusions & Outlook 175 176 Appendix A. Supplementary Moriond’12 results A.1. Event displays This section shows the details of the event displays of all events in the Moriond’12 dataset with pT(γ1) > 1 TeV. Only the hardest of these events enters CR1a (for SRs A, A’ and B). From lowest to highest pT(γ1) respectively, the event displays are shown in Figures A.1, A.2(a), A.2(b) and 5.11. None of them show ‘strange’ features to suspect they could originate from fake sources, e.g. non-collision backgrounds. Amongst the quantities checked to ensure this are: timing, cell quality, photon quality, no significant dead parts of the detector and the jet quality (e.g. timing, charged fraction, EM fraction, etc). Table A.1 outlines some of the details from these events. Run Event pT(γ1) pT(j1) pT(j2) pT(j3) E miss T ′ Number Number [TeV ] [TeV ] [TeV ] [GeV] [GeV] 189372 37505659 1.008 1.186 0.997 52 147 191426 151155403 1.046 1.238 1.081 48 115 190975 24668402 1.339 1.569 1.280 57 318 190236 87935353 1.406 1.645 1.146 185 297 Table A.1.: Details for the CR1a events in the Moriond’12 dataset with pT(γ1) > 1 TeV. The corresponding event displays are shown in Figures A.1, A.2(a), A.2(b) and 5.11 respectively. EmissT ′ is as defined in Section 5.4.1. 177 178 Supplementary Moriond’12 results Figure A.1.: Event displays of the first event in Table A.1 (pT(γ1) = 1.008 TeV). Supplementary Moriond’12 results 179 (a) (b) Figure A.2.: Event displays of (a) the second (pT(γ1) = 1.046 TeV) and (b) third (pT(γ1) = 1.339 TeV) events in Table A.1. 180 Appendix B. SMDP inclusive prompt photon cross-section measurement (35 pb−1) The aim of this section is to summarise some of the results from the latest published ATLAS prompt photon cross-section analysis, performed by the SMDP group, which are relevant to the ZfromGamma method and often quoted in the main sections. This analysis corresponds to 35 pb−1 and can be found preliminary documented in [76] (data from September-October 2010) and published in 2011 [49]. Further updates of this analysis with more data have been done but not published yet in a journal but rather presented at conferences e.g. EPS’11 [92]. Similarly, the first published analysis of this kind from ATLAS was in 2010 with 880 nb−1 [48] and its main difference with respect to the 35 fb−1 analysis is the exclusion of the region 1.81 ≤ |η| < 2.37 in the photon acceptance (see Table 5.8), which at the time suffered from relatively low εγid, large shower shape uncertainties and unsuitable MC simulation. The main contribution from the author to these analyses was in constantly presenting the ZfromGamma results to the SMDP group, which were always at the forefront of photon- based analyses, particularly concerning prompt photon events produced in association with jets (γ + jets). The ZfromGamma results therefore provided useful feedback to this group e.g. for the recent SMDP γ + jets cross-section measurement publication [98]. An additional contribution from the author was to produce some of the SMDP EPS’11 plots and results previously mentioned [92], specifically those presented in Section C.3.3. 181 182 SMDP inclusive prompt photon cross-section measurement (35 pb−1) B.1. Photon Selection As mentioned in Section 5.3, the event selection and object definitions used for Moriond’11 were practically identical to the those from the SMDP 35 pb−1 analysis. This selection is summarised in the corresponding Moriond’11 column in Tables 5.8-5.9. The only significant difference was the DQ criteria (GRL): in [49] fewer 2010 run periods were included (G-I only, amounting to 34.6± 1.2 pb−1), whereas the 0` analysis included all (A-I, see Table 5.2). The net loss in luminosity from not using period A-F is ∼ 3 pb−1 [49]. B.2. Efficiencies As a part of this study, we compare with the efficiency results in [49] and for this reason we summarise the main results in this section. In the reference, the overall photon efficiency is the product of three individually estimated efficiencies: reconstruction εγrec, identification εγid and trigger efficiency ε γ trig. Trigger Efficiency εγtrig- It is defined as the probability for a prompt photon candidate to pass the g40 loose trigger given that it passes the experimental isolation and identification requirements. The integrated efficiency for ET > 45 GeV and all η 1 bins was found to be (99.4+0.6−0.2)%, Figure B.1. Other triggers used for the subsequent analysis rounds have similar efficiencies, e.g. see Table 2.5 and [43]. Reconstruction Efficiency (εγrec) - This is the efficiency of reconstructing a photon given that it passes the cluster quality and experimental isolation requirements. It is computed as a function of ET and |η|. Table B.1 quotes these results, where efficiencies between 70% and 86% are observed. Unlike the identification efficiency (see below), εγrec decreases with ET for all |η|, as shown in Figure B.2. The decrease slows at high ET, as if reaching a plateau. Identification Efficiency (εγid) - This is the efficiency of true prompt photons to pass the identification, given that they pass the isolation requirement. It is also computed as a function of ET and |η|. Table B.2 quotes these results, where efficiencies between 90 and 97% are observed. Unlike εγrec, ε γ id increases with ET for all |η|, as shown in Figure B.3. This increase also slows at high ET, as if reaching a plateau. 1The η referred to in this appendix is the one computed in the second sampling of ATLAS LAr calorimeter and sometimes is also denoted as ηs2. SMDP inclusive prompt photon cross-section measurement (35 pb−1) 183 Tcluster E [GeV] 34 36 38 40 42 44 46 48 50 Ef fic ie nc y 0 0.2 0.4 0.6 0.8 1 MC Data ATLAS Figure B.1.: Photon trigger efficiency with respect to the offline photon selection as measured in data (black dots) and MC (empty dots) for the g40 loose trigger, on photon candidates passing the tight identification criteria and with isolation energy lower than 3 GeV. From [49]. 184 SMDP inclusive prompt photon cross-section measurement (35 pb−1) εγrec [%] ET [GeV] |η| ∈ [0− 0.6) |η| ∈ [0.6− 1.37) |η| ∈ [1.52− 1.81) |η| ∈ [1.81− 2.37) [45, 55) 85.5 ± 0.2 86.9 ± 0.1 77.2 ± 0.3 78.6 ± 0.2 [55, 70) 85.2 ± 0.2 86.6 ± 0.2 76.7 ± 0.4 78.0 ± 0.3 [70, 85) 85.2 ± 0.3 86.1 ± 0.3 75.6 ± 0.6 77.4 ± 0.4 [85, 100) 85.6 ± 0.2 85.5 ± 0.1 74.7 ± 0.3 76.1 ± 0.2 [100, 125) 85.1 ± 0.2 85.9 ± 0.2 75.0 ± 0.3 76.6 ± 0.2 [125, 150) 85.0 ± 0.3 85.2 ± 0.3 73.3 ± 0.6 75.0 ± 0.4 [150, 200) 84.8 ± 0.4 84.2 ± 0.3 71.3 ± 0.7 74.4 ± 0.6 [200, 400) 83.6 ± 0.2 83.4 ± 0.1 71.3 ± 0.3 73.7 ± 0.3 Table B.1.: Isolated prompt photon reconstruction efficiency εγrec as a function of true photon ET in four pseudorapidity intervals. The quoted errors are statistical only. From [49]. [GeV]T γTrue E 50 100 150 200 250 300 350 400 R e co n st ru ct io n Ef fic ie n cy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Direct photons Fragmentation photons MC10 simulation |<0.6γη| [GeV]T γTrue E 50 100 150 200 250 300 350 400 R e co n st ru ct io n Ef fic ie n cy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Direct photons Fragmentation photons MC10 simulation |<1.37γη|≤0.6 [GeV]T γTrue E 50 100 150 200 250 300 350 400 R e co n st ru ct io n Ef fic ie n cy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Direct photons Fragmentation photons MC10 simulation |<1.81γη|≤1.52 [GeV]T γTrue E 50 100 150 200 250 300 350 400 R e co n st ru ct io n Ef fic ie n cy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Direct photons Fragmentation photons MC10 simulation |<2.37γη|≤1.81 Figure B.2.: εγrec plots corresponding to the results in Table B.1. From [49]. SMDP inclusive prompt photon cross-section measurement (35 pb−1) 185 εγid [%] ET [GeV] |η| ∈ [0− 0.6) |η| ∈ [0.6− 1.37) |η| ∈ [1.52− 1.81) |η| ∈ [1.81− 2.37) [45, 55) 91.3 ± 0.1 93.2 ± 0.1 93.0 ± 0.2 89.9 ± 0.2 [55, 70) 93.1 ± 0.2 94.3 ± 0.1 94.4 ± 0.2 90.9 ± 0.2 [70, 85) 93.6 ± 0.2 94.9 ± 0.2 94.8 ± 0.3 91.1 ± 0.3 [85, 100) 94.6 ± 0.1 95.6 ± 0.1 95.8 ± 0.1 92.5 ± 0.1 [100, 125) 94.7 ± 0.1 96.2 ± 0.1 96.0 ± 0.2 91.3 ± 0.2 [125, 150) 95.1 ± 0.2 96.3 ± 0.1 95.0 ± 0.3 90.6 ± 0.3 [150, 200) 94.7 ± 0.2 96.7 ± 0.2 96.7 ± 0.3 91.5 ± 0.4 [200, 400) 95.2 ± 0.1 96.5 ± 0.1 97.0 ± 0.1 92.8 ± 0.1 Table B.2.: Central values of the εγid, after correcting the MC shower shapes to match those in data. These central values are computed for a mixture of direct and fragmentation photons from Pythia. The quoted errors are statistical only. From [49]. [GeV]γTE 50 100 150 200 250 300 350 400 Ef fic ie n cy 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 = 7 TeVsSimulation systematic uncertainty |<0.6γη| < 3 GeVisoTE ATLAS [GeV]γTE 50 100 150 200 250 300 350 400 Ef fic ie n cy 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 = 7 TeVsSimulation systematic uncertainty |<1.37γη|≤0.6 < 3 GeVisoTE ATLAS [GeV]γTE 50 100 150 200 250 300 350 400 Ef fic ie n cy 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 = 7 TeVsSimulation systematic uncertainty |<1.81γη|≤1.52 < 3 GeVisoTE ATLAS [GeV]γTE 50 100 150 200 250 300 350 400 Ef fic ie n cy 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 = 7 TeVsSimulation systematic uncertainty |<2.37γη|≤1.81 < 3 GeVisoTE ATLAS Figure B.3.: εγid plots (as a function of the reconstructed photon ET) for the results in Table B.2. From [49]. 186 SMDP inclusive prompt photon cross-section measurement (35 pb−1) B.3. Signal yield and Purity Even with the great capabilities of ATLAS to reconstruct and identify photons, there is of course, some background contamination in the selected photon sample, mainly from “QCD jets” (pi0 decays). Photons from these jets are expected to be less isolated than prompt ones, so the isolation variable EisoT is chosen as discriminating variable. The background contamination was estimated in this analysis using the “two-dimensional sidebands” (2D-sidebands) method, which uses the experimental shower shapes and EisoT to define one signal region (A) and three control regions (B, C and D). The signal yield is then defined as, N sigA = N obs A −NbkgA (B.1) The signal purity is defined as the signal yield from Equation (B.1) divided by the number of photon candidates in region A, which can also be re-expressed from the number of candidates seen in each region: P = N sigA NobsA = 1− N obs B N obs C NobsA N obs D (B.2) The obtained signal yield and corresponding purity are quoted, as functions of ET and η, in Table B.3 and plotted as a function of ET for the barrel η region in Figure B.4. The 2D-sidebands method assumes a negligible signal contamination in the control regions and that the shower shape variables and EisoT are uncorrelated. Table B.3 and the example purity plots in Figure B.4 clearly show the background decreases with increasing photon ET. This is to a large extent due to the isolation criteria, which is more efficient at large ET where jets are more collimated and it becomes less likely that for example an high-energy pi0 remains isolated. This can also be appreciated in the EisoT distributions in Figure B.5 where the background-enriched sample (non-tight candidates) extend to larger EisoT values in the high ET region compared to the signal-like (tight) candidates. Another potential source of background is W boson events, where an electron from the W boson decay is misidentified as a photon. This background is, however, highly ET dependent, due to the electron spectrum peaking approximately around ET = mW/2, and is therefore expected to be small for high ET photon events. The electron background was also found to be small in [49] and was hence neglected throughout the ZfromGamma analysis. SMDP inclusive prompt photon cross-section measurement (35 pb−1) 187 Signal yield ET range [ GeV] |ηs2| ∈ [0.00; 0.60) |ηs2| ∈ [0.60; 1.37) |ηs2| ∈ (1.52; 1.81) |ηs2| ∈ [1.81; 2.37) [45, 55) 22959± 176+2092−1686 28146± 215+3044−2809 10191± 118+1304−1336 17017± 172+2492−2276 [55, 70) 13629± 131+1091−887 16082± 154+1550−1450 5785± 85+598−700 9722± 126+1180−1143 [70, 85) 5052± 77+351−268 6256± 92+526−540 2210± 51+166−200 3581± 74+397−391 [85, 100) 2325± 51+139−114 2746± 57+201−211 916± 32+88−98 1592± 47+174−159 [100, 125) 1528± 41+100−74 1896± 47+131−159 594± 25+42−46 991± 36+101−93 [125, 150) 571± 25+28−25 705± 28+53−51 225± 16+19−22 323± 20+25−21 [150, 200) 361± 20+21−18 399± 21+35−34 135± 12+14−13 205± 16+17−22 [200, 400) 156± 13+11−11 188± 14+15−24 53± 7+5−7 56± 7+3−3 Purity ET range [GeV] |ηs2| ∈ [0.00; 0.60) |ηs2| ∈ [0.60; 1.37) |ηs2| ∈ (1.52; 1.81) |ηs2| ∈ [1.81; 2.37) [45, 55) 0.91+0.01+0.08−0.01−0.06 0.87 +0.01+0.08 −0.01−0.07 0.91 +0.01+0.09 −0.01−0.10 0.87 +0.01+0.12 −0.01−0.11 [55, 70) 0.93+0.01+0.06−0.01−0.04 0.90 +0.01+0.07 −0.01−0.05 0.94 +0.02+0.06 −0.02−0.09 0.89 +0.01+0.10 −0.01−0.09 [70, 85) 0.96+0.02+0.04−0.02−0.04 0.94 +0.02+0.06 −0.02−0.05 0.96 +0.03+0.04 −0.03−0.05 0.92 +0.02+0.08 −0.02−0.09 [85, 100) 0.97+0.03+0.03−0.03−0.03 0.97 +0.03+0.03 −0.03−0.04 0.97 +0.03+0.03 −0.05−0.03 0.93 +0.04+0.07 −0.04−0.07 [100, 125) 0.97+0.03+0.03−0.04−0.03 0.97 +0.03+0.03 −0.03−0.04 0.99 +0.01+0.01 −0.06−0.02 0.95 +0.05+0.05 −0.05−0.07 [125, 150) 0.98+0.02+0.02−0.06−0.02 0.99 +0.01+0.01 −0.05−0.04 0.98 +0.02+0.02 −0.09−0.03 0.97 +0.03+0.03 −0.08−0.04 [150, 200) 0.99+0.01+0.01−0.07−0.03 0.98 +0.02+0.02 −0.07−0.04 0.98 +0.02+0.02 −0.12−0.03 0.97 +0.03+0.03 −0.10−0.06 [200, 400) 1.00+0.00+0.00−0.11−0.02 0.98 +0.02+0.02 −0.10−0.03 1.00 +0.00+0.00 −0.20−0.03 1.00 +0.00+0.00 −0.19−0.02 Table B.3.: Signal yield and purity from the two-dimensional sidebands, for each |ηs2| region and ET interval. The first error is statistical, the second systematic. From [49]. 188 SMDP inclusive prompt photon cross-section measurement (35 pb−1) [GeV]TE 50 100 150 200 250 300 350 400 ] - 1 [ G eV T dN /d E 210 310 410 -1L dt = 35 pb∫ = 7TeV, s | < 0.60η| Data Systematics (a) [GeV]TE 50 100 150 200 250 300 350 400 ] - 1 [ G eV T dN /d E 210 310 410 -1L dt = 35 pb∫ = 7TeV, s | < 1.37η |≤0.60 Data Systematics (b) [GeV]TE 50 100 150 200 250 300 350 400 Si gn al P ur ity 0.5 0.6 0.7 0.8 0.9 1 ATLAS -1L dt = 35 pb∫ = 7TeV, s | < 0.60η| Data Systematics (c) [GeV]TE 50 100 150 200 250 300 350 400 Si gn al P ur ity 0.5 0.6 0.7 0.8 0.9 1 ATLAS -1L dt = 35 pb∫ = 7TeV, s | < 1.37η |≤0.60 Data Systematics (d) Figure B.4.: Signal yield and corresponding purity with statistical errors as a function of ET, for the barrel region region, as determined from the two-dimensional sidebands method in [49]. The yellow band represents the total systematic error. From [49]. SMDP inclusive prompt photon cross-section measurement (35 pb−1) 189 Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 1000 2000 3000 4000 5000 6000 -1L dt = 35 pb∫ = 7TeV, s | < 0.60η| < 55 GeVT E≤45 GeV Data, tight Data, non-tight ATLAS (a) Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -1L dt = 35 pb∫ = 7TeV, s | < 1.37η |≤0.60 < 55 GeVT E≤45 GeV Data, tight Data, non-tight ATLAS (b) Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 20 40 60 80 100 -1L dt = 35 pb∫ = 7TeV, s | < 0.60η| < 200 GeVT E≤150 GeV Data, tight Data, non-tight ATLAS (c) Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 20 40 60 80 100 120 -1L dt = 35 pb∫ = 7TeV, s | < 1.37η |≤0.60 < 200 GeVT E≤150 GeV Data, tight Data, non-tight ATLAS (d) Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 5 10 15 20 25 30 35 40 45 -1L dt = 35 pb∫ = 7TeV, s | < 0.60η| < 400 GeVT E≤200 GeV Data, tight Data, non-tight (e) Isolation [GeV] -5 0 5 10 15 20 25 30 35 En tri es /1 G eV 0 10 20 30 40 50 60 -1L dt = 35 pb∫ = 7TeV, s | < 1.37η |≤0.60 < 400 GeVT E≤200 GeV Data, tight Data, non-tight (f) Figure B.5.: The distributions for the calorimetric isolation variable EisoT , for tight (solid dots) and non-tight (open triangles) candidates in the barrel region (left column refers to |η| < 0.6, right column to 0.6 < |η| < 1.37). Top to bottom rows means from low to high ET (45 to 200 GeV). The non-tight distribution is normalized to the tight for EisoT > 5 GeV (non-isolated region). From [49]. 190 Appendix C. Results from Previous Analyses The aim of this appendix is to show some ZfromGamma results from previous analysis rounds (prior to Moriond’12) that are not provided in Chapter 5. The analyses will be presented as sub-sections in chronological order: Moriond’11, PLHC’11 and EPS’11. The structure/sectioning will be the same as in Chapter 5 and, unless otherwise stated, the general concepts discussed in the main sections apply to all these analyses. As mentioned in the introduction of Chapter 5, the author produced most of the ZfromGamma-related results presented in the following sections, including the R&D that was required for the production of MC samples listed. With respect to the 0` analysis, the author performed most of the work to obtain the CR1a-related results, except for the results presented in the sections titled “Context within the 0` analysis” which concerns the CR1a implementation into the 0` likelihood function, final background fitting and use for setting limits on SUSY models. All the results and plots showed from the other 0` CRs and SRs were done by other members from the 0` group in ATLAS. C.1. Moriond’11 (35 pb−1) This analysis corresponds to the first attempt to implement the ZfromGamma method for the first publication of the 0` analysis [58]. The first documentation of the ZfromGamma method therefore appears in the 0` supporting documentation, found in [63]. Overall, these first ZfromGamma results were promising in the sense that the data showed reasonably good agreement with some of the MC predictions; on the other hand, the MC samples used at the time were very limited and not very suited for this purpose (e.g. few generators and small statistics available, in particular after the 0` high-pT selections) and also many 191 192 Results from Previous Analyses aspects of the method were still in early developments. This was in fact a common trend of all the data-driven background estimation methods then, so within the 0` analysis, the results were used only to validate the MC predictions and constrain some uncertainties. Because ZfromGamma was at the forefront of photon analyses in ATLAS at the time, the required γ +X sample faced new issues which had not been covered by the SMDP analysis then [48], such as the increase in luminosity (35 pb−1 versus 0.880 pb−1) and pileup conditions, a higher photon-pT selection, and jet selections (the analysis in [48] was only inclusive), photon-jet overlap removal (see Section 5.4), the use of reconstructed EmissT in photon events, etc. C.1.1. Framework The framework used in this analysis is specified in Section 5.1 and Table 5.1. C.1.2. Event Samples Data: The data was in SUSYD3PD format and included 2010 data periods A-I, amounting to ∫ L dt ∼ 35 fb−1 after applying the Moriond’11 0` GRL (see Table 5.2). The data streams used are listed in Table C.1. Data Period Data Stream A-D L1Calo E-I Egamma Table C.1.: Data streams used in the Moriond’11 analysis. Monte Carlo: The MC samples available for this analysis are listed in Tables C.2-C.4 and the production details in Table 5.7. The ALPGEN signal samples had a 2-jet filter applied at generator level, making them useful only after the 0` “Dijet selection” had been applied (see Section C.1.4). The PYTHIA QCD sample contained fake photon candidates (e.g. pi0 and η decays) as well as prompt photon signal (e.g. produced by QED radiation emitted from quarks and by parton fragmentation). Another PYTHIA sample contained prompt photon signal from hard γ-jet scattering contributions (e.g. qq¯ → gγ or qg → qγ). Results from Previous Analyses 193 Regarding matching data conditions, at the time of Moriond’11 the inclusion of a pileup component had only been implemented in a few samples (see Table 5.7); in this case, only for the ALPGEN samples, and also there was no official pileup reweighing tool like in the later analyses. Nevertheless, pileup effects were found to have negligible effects in this dataset for the 0` analysis and ZfromGamma [63]. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 108081 PythiaPhotonJet Unbinned35 1.7305 · 10+4 0.60450 1.000 1998486 116390 AlpgenJimmyGamNp1 JetFilter Nj2Et20 7.4139 · 10+4 0.10870 1.000 199718 116391 AlpgenJimmyGamNp2 JetFilter Nj2Et20 2.1474 · 10+4 0.30995 1.000 199896 116392 AlpgenJimmyGamNp3 JetFilter Nj2Et20 5.8390 · 10+3 0.46646 1.000 199848 116393 AlpgenJimmyGamNp4 JetFilter Nj2Et20 1.6224 · 10+3 0.65008 1.000 199766 Table C.2.: Moriond’11 Monte Carlo samples used to simulate the γ + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 105807 JF35 pythia jet filter 5.4969 · 10+7 1.000 1.000 4583202 Table C.3.: Moriond’11 Monte Carlo samples used to simulate the SM background to the γ+ jets signal from QCD, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 115112 PythiaZnunuJet Pt20 1.2490 · 10+3 1.0 1.000 49890 107710 AlpgenJimmyZnunuNp0 pt20 filt1jet 3.5407 · 10+3 7.924433 · 10−3 1.000 2999 107711 AlpgenJimmyZnunuNp1 pt20 filt1jet 7.0170 · 10+2 0.6112469 1.000 44487 107712 AlpgenJimmyZnunuNp2 pt20 filt1jet 2.1700 · 10+2 0.8896797 1.000 39491 107713 AlpgenJimmyZnunuNp3 pt20 filt1jet 6.0160 · 10+1 0.9689922 1.000 11995 107714 AlpgenJimmyZnunuNp4 pt20 filt1jet 1.4640 · 10+1 0.9900990 1.000 7993 107715 AlpgenJimmyZnunuNp5 pt20 filt1jet 4.7100 · 10+0 0.998004 1.000 2500 Table C.4.: Moriond’11 Monte Carlo samples used to simulate the Zνν + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. 194 Results from Previous Analyses C.1.3. Inclusive Photon Sample (γ +X) Event Selection: A combined and more technical version of Tables 5.8 and 5.9 for Moriond’11 is shown in Table C.5. It can be seen that the selection was the same as in the SMDP 880 nb−1 analysis [48], with the exception of the items highlighted in bold, which were added in order to include all the data periods used in the 0` analysis (A-I). This was acceptable given the higher photon pT cut set in ZfromGamma compared to [48], ensuring unprescaled triggers with ∼ 100% efficiency. More clearly seen in Tables 5.8, the main difference in selection with respect to the later analyses was the smaller photon acceptance (|η| < 1.81, see Appendix B). The larger acceptance used in the later analyses therefore helped to reduce the required acceptance correction, entering the method through Aγ · εγ in Equation (5.8), shown in Table 5.17. Requirement Data MC Preselection GRL 0` GRL none Trigger g10 loose (A-E4 except 160975) g10 loose g20 loose (E5-F2 including 160975) g40 loose (G-I) Primary Vertex At least 1 primary vertex with ≥3 tracks same as in Data Acceptance |ηγ | < 1.37 or 1.52 ≤ |ηγ |1.81 (ηγ = ph etas2) “ pT > 45 GeV (pT = ph cl pt) Object Quality egamma::checkOQCluster OQmap (period I) Photon(run,ph cl eta,ph cl phi) < 3 Identification & Isolation Robust-Tight PhotonIDTool::PhotonCutsTight(3) same as in Data Isolation ph Etcone40 corrected < 3 GeV “ Table C.5.: Moriond’11 event selection for the γ + X sample. The selection is identical to [48, 114] except for the highlighted items. Results: The cutflow obtained for the γ +X selection is shown in Table 5.10, which was validated with the SMDP group results quoted in [114]. For all the plots in this section, the MC is from the PYTHIA samples listed in Section C.1.2 (the ALPGEN signal samples were not used at this stage due to the 2-jet filter already discussed). The γ+ jets signal is normalised to the data luminosity and cross-section while the QCD background is normalised so that the sum of signal and background match the data. Results from Previous Analyses 195 The corresponding pT, |η|, φ and shower shape distributions of the prompt-photon candidates passing the γ + X selection (Table C.2) are shown in Figures 5.3(b), C.1 and C.3 respectively. As a consistency check, for photon pT > 50 GeV in Figure 5.3(b), there are 80 730 candidates, which is comparable to the number quoted in [48] for the same luminosity (∼ 69 563), considering the SMDP number is after subtracting the background. As for the shower shape distributions, these were also consistent with the SMDP group equivalent found in [115] (the definitions of the shower shape variables can be found in [115] or [48]). The leading jet pT distribution for this γ +X sample is shown in Figure C.2. -2 -1.5 -1 -0.5 0 0.5 1 1.5 20 1000 2000 3000 4000 5000 6000 7000 8000 -1L dt ~ 35 pb∫DATA A-I γMC prompt MC QCD IRT_ph_cl_eta [GeV] En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV (a) -3 -2 -1 0 1 2 3 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 -1L dt ~ 35 pb∫DATA A-I γMC prompt MC QCD IRT_ph_cl_phi [GeV] En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV En tri es /0 .1 4 G eV (b) Figure C.1.: (a) Moriond’11 |η| and (b) φ distributions for the prompt photon candidates in the γ +X sample (Figure 5.3(b)). 0 100 200 300 400 500 600 700 800 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD A_J1_Pt [GeV] En tri es /5 .0 G eV En tri es /5 .0 G eV Figure C.2.: Moriond’11 leading jet pT distribution in the γ +X sample. 196 Results from Previous Analyses 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 210 310 410 510 -1L dt ~ 35 pb∫ IRT_ph_eratio [GeV] En trie s/0 .02 5 G eV DATA A-I γMC prompt MC QCDEn trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_f1 [GeV] En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_fside [GeV] En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 510 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_reta [GeV] En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 510 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_rphi [GeV] En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (e) 0 0.0020.0040.0060.008 0.010.0120.0140.0160.0180.02 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_weta2 [GeV] En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV En trie s/0 .00 05 G eV (f) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 410 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_ws3 [GeV] En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV En trie s/0 .02 5 G eV (g) 0 0.5 1 1.5 2 2.5 3 3.5 4 -110 1 10 210 310 410 510 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD IRT_ph_wstot [GeV] En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V En trie s/0 .1 Ge V (h) Figure C.3.: Moriond’11 distributions of shower shape variables used in the “Robust-Tight” photon identification (Table C.5) for the prompt photon candidates in the γ +X sample. Results from Previous Analyses 197 C.1.4. Control Region Sample (CR1a) CR1a object definition: This is specified in Section 5.4.1. 0` Selection: Having applied the CR1a object definitions (Section 5.4) and 0` object definitions in [63], the 0` event selection applied is summarised in Table C.6 (a more detailed version can be found in [63]). Four signal regions A, B, C and D were defined (targeting light-q˜q˜, heavy-q˜q˜, g˜g˜ and g˜q˜ production, respectively). The “Pre-selection” without the EmissT requirement defined in this case the Control Region (CR). The moti- vation for this was that the statistics in this CR were much larger that in the SR and hence a more precise cross-check between the data and MC could be made. A B C D P re -s el ec ti on Number of required jets ≥ 2 ≥ 2 ≥ 3 ≥ 3 Leading jet pT [GeV] > 120 > 120 > 120 > 120 Other jet(s) pT [GeV] > 40 > 40 > 40 > 40 EmissT [GeV] > 100 > 100 > 100 > 100 F in al se le ct io n ∆φ(jet, EmissT )min > 0.4 > 0.4 > 0.4 > 0.4 EmissT /meff > 0.3 – > 0.25 > 0.25 meff [GeV] > 500 – > 500 > 1000 mT2 [GeV] – > 300 – – Table C.6.: Moriond’11 Criteria for admission to each of the four overlapping Signal Regions A to D. All variables are defined in [58]. Results: For this part, some relevant results have been discussed in Section 5.4. Once the full CR1a selection is applied on the γ + X sample, the remaining background is quite small, as shown in Figure 5.3(b) by the good agreement of data with MC signal. For this reason (as well as for the lack of suitable high-pT background samples during this time), the plots that follow only show the γ + jets MC signal from PYTHIA and ALPGEN (the latter only if a ≥ 2 jet selection has been applied) and the normalisation is to the data luminosity and cross-section. Figure C.4 shows the evolution with the 0` selections (up to the CR stage, known as the “Dijet selection”, see above) for channels A and C of pT(γ1) and the redefined E miss T = pT(γ1) +E fake T ′ (the latter being like a smeared version of pT(γ1), see Equations 5.1-5.3). Figures C.4(a)-C.4(b) show a very good agreement between data and the PYTHIA signal already at the γ+X selection stage – a confirmation 198 Results from Previous Analyses that the background left is small. However, Figures C.4(c)-C.4(d) show that once the dijet selection is applied, a discrepancy between data and the PYTHIA signal becomes evident at low-pT. In contrast, the ALPGEN signal does not suffer from this problem. Given that the data-PYTHIA discrepancy was found to be mitigated at higher photon-pT and lower jet multiplicities, it was thought to be due to missing multijet events in PYTHIA. To further support this, a similar trend is observed for the leading jet-pT, shown in Figure C.5, where in this case, the data-PYTHIA discrepancy is significant even before the dijet selection (Figure C.5(a)), and appears to grow with increasing pT (contrary to the case of pT(γ1)). Moreover, Figure C.2, which is equivalent to Figure C.5(a) but without including the QCD MC, further confirms that such discrepancy cannot be due to QCD background remnants but rather to the suspected missing multijet events in the PYTHIA signal. Figure C.4(e) shows the final CR1a pT(γ1) distribution for SR-A. In this case, the data-PYTHIA signal agreement is restored given the high pT(γ1) involved, e.g. see Table 5.16. The number of CR1a data events for each SR is shown in Table C.7 (column 3). In summary, the lack of multijet events was understood and was not because of problems with the PYTHIA model. Roughly speaking, the PYTHIA sample only contains events with pT(j2) < pT(γ), and the observed effect is due to the lack of events with the opposite pT configuration. Such events should be produced by the dijet processes, with a photon produced by the parton shower, however, this contribution was not available statistically enough for this analysis. Results from Previous Analyses 199 [GeV]γ T p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 410 510 γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (a) ) [GeV]missT, ET γVectorSum(p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 410 510 γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (b) [GeV]γ T p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 γMC Alpgen γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (c) ) [GeV]missT, ET γVectorSum(p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 γMC Alpgen γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (d) [GeV]γ T p 0 100 200 300 400 500 600 700 800 Ev en ts / 50 .0 G eV -110 1 10 210 γMC Alpgen γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (e) Figure C.4.: Moriond’11 Left: pT(γ1) distribution for (a) the γ + X sample, (c) γ + X sample after the 0` dijet selection and (e) after the full 0` selection for SR-A. Right: The same distributions as on the left but after adding EfakeT ′ (see Section 5.4.1). The MC shown is the PYTHIA and ALPGEN signal. 200 Results from Previous Analyses [GeV] T Leading Jet p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 410 510 γMC Alpgen γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (a) [GeV] T Leading Jet p 0 100 200 300 400 500 600 700 800 Ev en ts / 20 .0 G eV -110 1 10 210 310 γMC Alpgen γMC Pythia DATA -1L dt ~ 35 pb∫ATLAS Work in Progress (b) Figure C.5.: Moriond’11 Leading jet pT distribution for (a) the γ + X sample and (b) the γ +X sample after the 0` dijet selection. (a) is the same as Figure C.2 but without including the QCD MC. Results from Previous Analyses 201 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10 210 310 410 510 -1L dt ~ 35 pb∫ IRT_ph_eratio [GeV] En tri es /0 .0 25 G eV DATA A-I γMC prompt MC QCD En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 310 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD J2_ph_eratio [GeV] En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -110 1 10 210 -1L dt ~ 35 pb∫ DATA A-I γMC prompt MC QCD J2MET_ph_eratio [GeV] En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV En tri es /0 .0 25 G eV (c) Figure C.6.: Moriond’11 Effect of 0` selections on Eratio – a shower shape variable used to make the photon identification. The plots show a beneficial impact on εγid since slightly higher values are expected from the narrower shape. (a) γ +X sample; (b) γ +X sample with 0` Dijet selection and (c) γ + X sample with 0` Dijet and EmissT selections. The MC shown is from PYTHIA. 202 Results from Previous Analyses C.1.5. Transfer Function (TFZνν) Unlike in the current implementation of the method, where the Aγ(pT) · εγ(pT) and RZ/γ factors in the TF (Equation (5.6)) are obtained from prompt photon MC, during this time these values had to be obtained by other means because, as already emphasised, the prompt photon MC samples available then were not suited for such purposes. • Efficiency and Acceptance: A separate value for efficiency and acceptance had to be estimated (unlike the current implementation where the combined Aγ(pT) ·εγ(pT) value is obtained). For the reasons already discussed in Sections 5.4.3 and 5.5.1, an overall efficiency value εγ was estimated from the SMDP prompt photon results in [48] as a pT-η weighted-average of εγrec · εγid, resulting in a fixed value of ∼ 80%. To further support this procedure (and as complement to the discussion of Figure 5.8) the evolution of another shower shape variable Eratio (the asymmetry between the first and second maxima in the energy profile along η in the ATLAS ECAL) used for the photon ID requirement in Table C.5 is shown in Figure C.6. Again the 0` selections reassure the εγid value from SMDP results can be used on the final CR1a sample as a conservative value. Regarding the acceptance correction Aγ, as discussed, given that the γ and Zνν η distributions converge at high-pT (Figure 5.15), this correction is only to counteract the effect of the γ + X selection in the SRs, which the Zνν is not subjected to. Hence, Aγ was calculated as the fraction in Figure 5.15 that fell outside the η range considered in the γ +X selection. The result was cross-checked with the ratio of the pT(γ1) distributions in CR1a with and without the γ + X selection step (see Equation (5.8)). The average value obtained was ∼ 75%. • Purity: The value was also taken from the SMDP prompt photon results in [48] as a pT-η weighted-average resulting in a fixed value of ∼ 90%. • Z/γ Ratio: The value taken was from the then available result from GAMBOS, which at the time did not account for the variation in jet multiplicity. Results from Previous Analyses 203 TF stand-alone estimate of Zνν + jets: After the direct application of the TF to the CR1a event counts, the Zνν + jets background estimate results obtained for this analysis are shown in Table C.7 compared to PYTHIA and ALPGEN1. Despite the missing multijet events in PYTHIA discussed in Section C.1.4, this effect is mitigated in the SRs where only the high-pT photon events are selected, and in particular SR-A which has the lowest jet multiplicity. Indeed, the results show that the data was consistent with PYTHIA. However, at this stage a data-ALPGEN discrepancy is observed (the MC statistical uncertainty is not shown but can be assumed to be smaller and the luminosity uncertainty was ∼ 11%). This data-ALPGEN discrepancy was investigated further and it was found to appear after the meff cut (the last cut in the 0` selection). As an example, for the dijet channel (the one with the highest statistics), after the “Preselection” (see Table C.6), the ALPGEN result was 679 vs 657±26 in data, whereas with the full selection, the discrepancy became larger (85 vs 60± 8). The corresponding distributions for these results are shown in Figure C.7 in the form of an estimated Zνν + jets E miss T distribution for SRs A, C and D compared directly with the Zνν + jets signal (note that in the later analysis rounds, this kind of plots are show as a function of meff rather than E miss T ). Due to the fixed value of photon efficiency used, this estimate should be more precise for EmissT ∼>100 GeV. The integral of these distributions represents the number of Zνν + jets events quoted in columns 5 and 6 of Table C.7. SR meff CR1a Zνν + jets Estimate Zνν + jets Signal data Pythia/Alpgen data Pythia/Alpgen Pythia/Alpgen A 500 60 63.4 / 85.6 22± 5 26± 4 / 34 24 / 45 C 500 39 24.4 / 47.4 13± 4 10± 1 / 18 10 / 25 D 1000 1 0.6 / 3.8 0.5 0.3 / 1.8 0.0 / 0.8 Table C.7.: Moriond’11 numbers of CR1a events from data and MC for each SR (columns 3-4) and the stand-alone estimate of Zνν + jets background in the SRs from data and MC (columns 5-6), compared to Zνν + jets MC (column 7). The MC statistical uncertainty is not shown but can be assumed to be small. The luminosity uncertainty was then ∼ 11%. 1The results for SR-B are not shown because at the time the code to calculate the mT2 variable in Table C.6 had not been implemented in the ZfromGamma framework. 204 Results from Previous Analyses MET [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 50 .0 G eV 1 10 -1L dt ~ 35 pb∫ATLAS Work in Progress Data Est. MC Alpgen Est.γ MC Pythia Est.γ MC AlpgenννZ MC PythiaννZ (a) MET [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 50 .0 G eV 1 10 210 -1L dt ~ 35 pb∫ATLAS Work in Progress Data Est. MC Alpgen Est.γ MC Pythia Est.γ MC AlpgenννZ MC PythiaννZ (b) MET [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 50 .0 G eV 1 10 210 310 -1L dt ~ 35 pb∫ DATA AlpgenγMC PythiaγMC MC Zvv Alpgen MC Zvv Pythia (c) Figure C.7.: Moriond’11 Zνν + jets EmissT distributions in (a) SR-A, (b) SR-C, and (c) SR-D, from data and MC as estimated from CR1a using the TF, compared directly with Zνν + jets MC from PYTHIA and ALPGEN. The labels ‘Data’ and ‘MC γ Alpgen/Pythia’ indicate the TFs were applied to the CR1a data or MC events, whereas those labeled ‘Zνν + jets Alpgen/Pythia’ show the raw MC Zνν + jets estimates for the SRs scaled to the data luminosity. Results from Previous Analyses 205 C.1.6. Context within the 0` analysis Having been the first SUSY 0` analysis with ATLAS data, data-driven background estimation methods were in early developments at the time. Hence, the results from these methods were used only to validate the MC prediction and constrain some uncertainties, but the central value for the background estimate was taken from MC as shown in the 0` SRs meff distributions in Figure C.8 and represented numerically in Table C.8. From these, it was clear that the Z + jets and W + jets were the most dominant backgrounds, which further motivated the developments of the data-driven methods to estimate them, such as ZfromGamma. Similarly, this was also the first implementation of the ZfromGamma method and as mentioned, data-ALPGEN discrepancies had been found. At the time, CR1b was found more consistent with the Zνν + jets ALPGEN result and there were also published ATLAS W/Z results supporting the good agreement of data with ALPGEN [59]. This therefore motivated additional cross-checks of the method, like the ‘Zµµ cross-check’ described in Appendix D.1. In the end, the 0` results (Table C.8) were used to make the two interpretations shown in Figure C.9 (in a simplified and a constrained mSUGRA model, briefly explained in Section 5.6 and Section 1.2.2). En tri es / 10 0 G eV -110 1 10 210 310 410 510 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV = 7 TeV)sData 2010 ( SM Total multi−jet W+jets Z+jets and single toptt SM + SUSY reference point -1L dt ~ 35 pb∫ Signal region A 2 jets)≥( ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A/ SM 0 0.5 1 1.5 2 2.5 D AT A/ SM En tri es / 10 0 G eV -110 1 10 210 310 410 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV = 7 TeV)sData 2010 ( SM Total multi−jet W+jets Z+jets and single toptt SM + SUSY reference point -1L dt ~ 35 pb∫ Signal regions C & D 3 jets)≥( ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 D AT A/ SM 0 0.5 1 1.5 2 2.5 D AT A/ SM Figure C.8.: Moriond’11 meff distribution for channels A and C/D prior to the meff cut (red arrows mark the start of a SR), in data and MC (W/Z + jets is from ALPGEN, tt¯ and single top from MC@NLO and QCD from PYTHIA) and a mSUGRA reference point with m0 = 200 GeV, m1/2 = 190 GeV, A0 = 0, tanβ = 3 and µ > 0. Black vertical bars show the statistical uncertainty from the data, while the yellow band shows the size of the SM MC uncertainty. From [58]. 206 Results from Previous Analyses Signal region A Signal region B Signal region C Signal region D QCD 7 +8−7[u+j] 0.6 +0.7 −0.6[u+j] 9 +10 −9 [u+j] 0.2 +0.4 −0.2[u+j] W+jets 50± 11[u] +14−10[j]± 5[L] 4.4± 3.2[u] +1.5−0.8[j]± 0.5[L] 35± 9[u] +10− 8[j]± 4[L] 1.1± 0.7[u] +0.2−0.3[j]± 0.1[L] Z+jets 52± 21[u] +15−11[j]± 6[L] 4.1± 2.9[u] +2.1−0.8[j]± 0.5[L] 27± 12[u] +10− 6[j]± 3[L] 0.8± 0.7[u] +0.6−0.0[j]± 0.1[L] tt¯ and t 10± 0[u] + 3− 2[j]± 1[L] 0.9± 0.1[u] +0.4−0.3[j]± 0.1[L] 17± 1[u] + 6− 4[j]± 2[L] 0.3± 0.1[u] +0.2−0.1[j]± 0.0[L] Total SM 118± 25[u] +32−23[j]± 12[L] 10.0± 4.3[u] +4.0−1.9[j]± 1.0[L] 88± 18[u] +26−18[j]± 9[L] 2.5± 1.0[u] +1.0−0.4[j]± 0.2[L] Data 87 11 66 2 Table C.8.: Moriond’11 Expected and observed numbers of events in the four 0` SRs. Un- certainties shown are due to MC statistics, statistics in CRs, other sources of uncorrelated systematic uncertainty, and also the JER and lepton efficiencies [u], the JES [j], and the luminosity [L]. From [58]. gluino mass [GeV] 0 250 500 750 1000 1250 1500 1750 2000 sq ua rk m as s [G eV ] 0 250 500 750 1000 1250 1500 1750 2000 }CMSSMMSUGRA / = 10 pbSUSYσ = 1 pbSUSYσ = 0.1 pbSUSYσ =7 TeVs, -1 = 35 pbintL 0 lepton combined exclusion ATLAS q~LEP 2 Tevatron, Run I D0, Run II CDF, Run II Observed 95% C.L. limit Median expected limit σ1 ±Expected limit [GeV]0m 200 400 600 800 1000 [G eV ] 1/ 2 m 150 200 250 300 350 400 (400)g~ (600)g~ (800)g~ (400) q~ (600) q~ (800) q~ =7 TeVs, -1 = 35 pbintL 0 lepton combined exclusion ATLAS Reference point ± l~LEP 2 1 ± χ∼LEP 2 2 0χ ~, 1 ± χ∼D0 -1<0, 2.1 fbµ, q~, g~D0 -1<0, 2 fbµ=5, β, tanq~,g~CDF Observed 95% C.L. limit Median expected limit σ1 ±Expected limit -1 , 35 pbTαCMS Figure C.9.: Moriond’11 95% CLs exclusion limits obtained by using the SR with the best expected sensitivity at each point in a simplified MSSM scenario with only strong production of gluinos and first- and second-generation squarks, and direct decays to jets and neutralinos (left); and in the (m0 ; m1/2) plane of MSUGRA/CMSSM for tanβ = 3, A0 = 0 and µ > 0 (right). The red lines show the observed limits, the dashed-blue lines the median expected limits, and the dotted blue lines the ±1σ variation on the expected limits. Comparison with previous limits is illustrative only as some are derived in a different context. From [58]. Results from Previous Analyses 207 C.2. PLHC’11 (165 pb−1) The results for this 0` analysis were not published but rather presented at the PLHC’11 conference [65]2. One highlight was that this was the first 0` analysis using 2011 data (Moriond’11 used 2010 data). The corresponding ZfromGamma results were then docu- mented in the PLHC’11 0` internal note [102]. By this time, the ZfromGamma method had several improvements with respect to Moriond’11: new and more suitable MC samples, an improved photon selection and a better estimation of the TF; so the results, this time being significantly more solid and congruent, were used as the main Zνν + jets background estimate in the 0` analysis. As for 0` analysis itself, the main changes with respect to Moriond’11 were: • The use of the data-driven methods to estimate the SM background (rather than from MC as previously done) from CRs (now defined from selections as close as possible to the SR but enriched in particular background processes) and TFs. In this case, five CRs were defined per SR. • The introduction of a combined fit based on a likelihood function to obtain the total SM expectation. This fit accounted for CRs and SRs correlations and mutual- contamination. • New SRs with increased sensitivity (from larger jet multiplicities and harder pT cuts). • Updated 0` object definitions. • The use of a “pileup reweighing” tool on the MC to match better the data conditions. C.2.1. Framework The framework used in this analysis is specified in Section 5.1 and Table 5.1. C.2.2. Event Samples Data: The data was in SUSYD3PD format and included 2011 data periods B-D, amount- ing to ∫ L dt ∼ 165 pb−1 after applying the PLHC’11 0` GRL (more details in Table 5.2). 2In this reference, CR1a was referred to as ‘CR1’ (see Section C.2.6), but here ‘CR1a’ will be kept to remain consistent with the rest of the sections. 208 Results from Previous Analyses Monte Carlo: The MC samples used in this analysis are listed in Tables C.9-C.10 and the production details in Table 5.73. The new highlight was the availability of SHERPA samples for γ + jets and Zνν + jets. However, as suggested by the number of events generated and the plots below, their statistics at high-pT were relatively poor and the PYTHIA γ + jets was better in this regard. On the other hand, as discussed in Appendix C.1, the PYTHIA signal suffered from missing multijet events, so for this analysis it was only used for illustration of such effect and to support the data-MC agreement at high-pT where SHERPA lacked statistics. Another difference with respect to Moriond’11 was that samples to model the backgrounds to the γ + jets signal were no longer included in the plots. This was accepted at the time given the high-purity of the photon sample, in particular with the harder PLHC’11 SRs selections, as well as time constrains from the ATLAS MC production group to produce these samples. As for Zνν + jets MC, the PYTHIA sample was stopped and instead a SHERPA sample was used to be consistent with the γ + jets SHERPA estimate. The Zνν + jets ALPGEN samples used in Moriond’11 were still used for comparison purposes. Regarding matching the new data-conditions, the MC production for PLHC’11 had more appropriate characteristics to match the pileup conditions such as an added pileup component (“mc10a” in Table 5.7) and a “pileup reweighing” (PR) tool also became available. At the time this tool was still in early developments and it was found to introduce an inefficiency of ∼ 50% on the MC statistics [102]. In all the plots that follow, the MC is normalised to the data luminosity using the cross-sections listed and, unless otherwise stated, the PR tool is implemented using the “BCID-averaged reweighing”, which was the default in the 0` analysis. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 108081 PythiaPhotonJet Unbinned35 1.7305 · 10+4 0.60450 1.000 999752 113715 SherpaY4JetsPt70 1.5634 · 10+3 1.000 1.000 199930 Table C.9.: PLHC’11 Monte Carlo samples used to simulate the γ+ jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. 3Although some samples might appear to be the same in different analysis rounds, e.g. the PYTHIA signal in Tables C.9 and C.2, in general they have different production settings. Results from Previous Analyses 209 Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 119932 Z5jetstonunu30GeVScaleMT 5.2941 · 10+3 1.0 1.000 1699681 107710 AlpgenJimmyZnunuNp0 pt20 filt1jet 3.5407 · 10+3 7.924433 · 10−3 1.000 2999 107711 AlpgenJimmyZnunuNp1 pt20 filt1jet 7.0170 · 10+2 0.6112469 1.000 44487 107712 AlpgenJimmyZnunuNp2 pt20 filt1jet 2.1700 · 10+2 0.8896797 1.000 39491 107713 AlpgenJimmyZnunuNp3 pt20 filt1jet 6.0160 · 10+1 0.9689922 1.000 11995 107714 AlpgenJimmyZnunuNp4 pt20 filt1jet 1.4640 · 10+1 0.9900990 1.000 7993 107715 AlpgenJimmyZnunuNp5 pt20 filt1jet 4.7100 · 10+0 0.998004 1.000 2500 Table C.10.: PLHC’11 Monte Carlo samples used to simulate the Zνν + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. C.2.3. Inclusive Photon Sample (γ +X) Event Selection: At the time, the “new” SMDP analysis with 35 pb−1 had just come out as an update of the 880 nb−1 analysis but it had not yet been strictly finalised, so the selection used by ZfromGamma from the preliminary documentation in [116] and outlined in Tables 5.8 and 5.9. The main changes with respect to Moriond’11 can be seen to be a larger photon acceptance (up to |η| < 2.37, see Appendix B) and a higher photon-pT cut to suit the lowest unprescaled photon trigger for the new data periods included. Results: The cutflow obtained for the γ +X selection is shown in Table 5.10, which was validated with the SMDP group results in [116,117]. The pT distribution of the prompt photon candidates is shown in Figure C.10, where the good agreement of the data and the MC signal again corroborates the high-purity of the γ +X sample. Also in Figure C.10, at low-pT the data/MC ratio is lower for SHERPA than for PYTHIA, suggesting a potential overestimation from SHERPA of the γ +X cross-section – PYTHIA seems more “data-like” since more background is expected at low-pT, such as the Moriond’11 result in Figure 5.3(b). However, because both quickly converge around pT(γ1) ∼ 150 GeV this was not investigated further. C.2.4. Control Region Sample (CR1a) 0` selection: Having applied the CR1a object definitions (Section 5.4) and 0` object definitions in [102], the 0` event selection applied is summarised in Table C.11 (the detailed version can be found in [102]). Five SRs were defined: SR-A was identical to Moriond’11 SR-A but with a harder meff cut, SR-B was identical to Moriond’11 210 Results from Previous Analyses ph_pt [GeV]0 100 200 300 400 500 600 700 800 900 Ev en ts / 20 .0 G eV 1 10 210 310 410 510 610 +jets Pythiaγ +jets Sherpaγ Data 2011 -1L dt ~ 165 pb∫ ph_pt [GeV] 0 100 200 300 400 500 600 700 800 900 D AT A/ M C 0 0.5 1 1.5 2 2.5 DATA/Pythia DATA/Sherpa Figure C.10.: PLHC’11 pT distribution in data and MC of the prompt photon candidates in the γ +X sample. The MC shown are the PYTHIA and SHERPA signals. SR-D. The four-jet SRs were all new. Note that SR-E used an ‘inclusive’ version of meff , meff(incl.), which includes all jets with pT > 40 GeV, and was in fact the first time the 0` analysis used meff(incl.) before becoming the default last cut in Moriond’12. Regarding the motivations to define these SRs, the jet multiplicity is motivated from the expected final states of q˜q˜, q˜g˜ and g˜g˜ production, mainly resulting in dijet, three-jet and four-jet events respectively, e.g. from q˜ → qχ˜01 and g˜ → qqχ˜01 (see Section 1.2.2). Cascade decays tend to increase the final-state multiplicity. The motivation for the ∆φ, EmissT /meff and meff cuts is discussed briefly in Section 5.4.2 and more explicitly in the 0` documentation. SR-C and D were defined to increase sensitivity to different SUSY mass splittings, while the hardest SR, SR-E, was defined to boost the reach in the SUSY mass scale. Results: For this part, some relevant results have been discussed in Section 5.4. Fig- ure C.11 shows the prompt photon pT evolution with the 0` selections to define SR-A. Figure C.11(a) shows that at the stage of the γ +X selection, the data already agrees quite well with both the PYTHIA and SHERPA signals. However, at the dijet selection stage (Figure C.11(b)), the missing multijet events in PYTHIA become evident (see Sec- tion C.1.4), whereas SHERPA does not show such a problem. This effect is more dramatic when looking at the pT distribution of the softer jets in the event at this stage, like Figure C.12 which shows the effect is related to the second-leading jet (Figure C.12(b)) Results from Previous Analyses 211 Requirement Signal Region A B C D E EmissT [GeV] > 130 Leading selected jet pT [GeV] > 130 Second selected jet pT [GeV] >40 >40 >40 >40 >80 Third selected jet pT [GeV] – >40 >40 >40 >80 Fourth selected jet pT [GeV] – – >40 >40 >80 ∆φ (i = 1, 2(, 3)) >0.4 EmissT /meff > 0.3 (2j) > 0.25 (3j) > 0.25 (4j) > 0.25 (4j) > 0.2 (4j) meff [GeV] > 1000 (2j) > 1000 (3j) > 500 (4j) > 1000 (4j) > 1100 (incl.) Table C.11.: PLHC’11 0` SRs event selections. The quantities are defined elsewhere in the text or can be found in [102]. whereas the leading jet distribution is only scaled (Figure C.12(a)). This effect is not due to a lack of statistics in the PYTHIA sample – Figure C.11(a) and Figure C.11(b) clearly show SHERPA has less high-pT statistics than PYTHIA, and similarly the data-PYTHIA agreement is reasonably restored once the EmissT cut is applied (Figures C.11(c)-(d)). Figure C.13 shows an example CR1a pT(γ1) distribution for SR-C. Also shown in this figure, is the effect of the PR tool already mentioned, which clearly causes a significant loss in MC statistics. The typical percentage losses are quoted in Table C.12 for γ + jets SHERPA. The CR1a meff distributions (prior to the meff cut) for each SR are shown in Figure C.14 where good data-MC signal agreement is seen, despite the limited MC statistics. The corresponding number of events are shown in Table C.15 for both data and MC (columns 2 and 3). The average photon-pT and range of these events are quoted in Table 5.16. Signal Region MC statistics loss A 41% B 21% C 10% D 47% E 100% Table C.12.: PLHC’11 percentage loss in MC statistics from using the PR tool on the γ + jets SHERPA sample. For SR-C this effect is shown in Figure C.13. 212 Results from Previous Analyses ph_pt [GeV] 0 100 200 300 400 500 600 700 800 900 Ev en ts / 20 .0 G eV 1 10 210 310 410 510 610 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ (a) J2_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 900 Ev en ts / 20 .0 G eV 1 10 210 310 410 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Dijet channel (b) J2MET_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 40 .0 G eV 1 10 210 310 410 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Dijet channel (c) J2CR_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 40 .0 G eV 1 10 210 310 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Dijet channel (d) Figure C.11.: PLHC’11 prompt photon pT evolution with the CR1a selection for SR-A: (a) on the γ +X sample (230 457 events), (b) after the dijet selection (8 557 events), (c) after the dijet selection and EmissT cut (3 379 events), and (d) after the dijet selection, E miss T cut and a softer meff cut (500 GeV). The MC shown are the PYTHIA and SHERPA signals. J2_J0_pt [GeV] 0 100 200 300 400 500 600 700 800 900 Ev en ts / 20 .0 G eV 1 10 210 310 410 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Dijet channel (a) J2_J1_pt [GeV] 0 100 200 300 400 500 600 700 800 900 Ev en ts / 20 .0 G eV 1 10 210 310 410 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Dijet channel (b) Figure C.12.: PLHC’11 effect of missing multijets in γ + jets PYTHIA for the (a) leading and (b) second-leading jet pT. Results from Previous Analyses 213 SR3_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 40 .0 G eV 1 10 210 +jets MC Pythiaγ +jets MC Sherpaγ =7 TeV)sData 2011 ( -1L dt ~163 pb∫ Four Jet channel (a) SR3_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 Ev en ts / 40 .0 G eV 1 10 210 +jets Pythiaγ +jets Sherpaγ =7 TeV)sData 2011 ( -1L dt ~165 pb∫ Four Jet channel (b) Figure C.13.: PLHC’11 prompt photon pT distribution in SR-C, showing the effect of using the pileup reweighing (PR) tool on the MC: (a) without PR and (b) with PR, where a drop in MC statistics is clear. The MC shown is the PYTHIA and SHERPA signal. 214 Results from Previous Analyses En tri es / 10 0 G eV 1 10 210 310 410 510 =7 TeV)sData 2011 ( +jetsγ -1L dt ~165 pb∫ Dijet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (a) En tri es / 10 0 G eV 1 10 210 310 410 510 =7 TeV)sData 2011 ( +jetsγ -1L dt ~165 pb∫ Three Jet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (b) En tri es / 10 0 G eV 1 10 210 310 410 510 =7 TeV)sData 2011 ( +jetsγ -1L dt ~165 pb∫ Four Jet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (c) En tri es / 10 0 G eV 1 10 210 310 410 510 =7 TeV)sData 2011 ( +jetsγ -1L dt ~165 pb∫ Four Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (d) Figure C.14.: PLHC’11 CR1a meff distributions in data and MC for SR-A (a), B (b) and C/D (c) and E (d). The MC shown is the SHERPA signal. The yellow band in the data/MC ratio denotes the size of the combined JER/JES and MC statistical uncertainties quoted in Tables C.13 and C.15 respectively. Results from Previous Analyses 215 C.2.5. Transfer Function (TFZνν) For this part, the highlight was that this was the first time for which it was possible to obtain part of the TF from MC rather than assuming SMDP results. The TF central values and associated uncertainties obtained are shown in Table C.13 and a summary of the procedures to calculate each of the factors now follows. CR1a TF central value & uncertainties SR A B C D E Central Value 0.375 0.371 0.305 0.371 0.340 CR bckgrnd. (fbkg) 3% 3% 3% 3% 3% Aγ · εγ 22% 14% 7% 22% 30% ηZ/γ 2% 2% 2% 2% 2% JES/JER +1.4−2.6 % +1.4 −2.6 % +1.4 −2.6 % +1.4 −2.6 % +1.4 −2.6 % Pileup 4% 4% 4% 4% 4% Trigger < 1% < 1% < 1% < 1% < 1% Theory (RZνν/γ) 15% 15% 15% 15% 15% Table C.13.: PLHC’11 Central values and associated uncertainties of the CR1a TFs. The meaning of the terms are explained elsewhere in the text. • Efficiency and Acceptance: These were also estimated for the first time using a bin-by-bin unfolding approach and as a combined Aγ · εγ correction factor to the TF as currently done. The original aim was to calculate it after the full CR1a selection to include all the effects arising from the SRs selections, as done in the current implementation (Section 5.5.1). However, due to the lack of MC statistics already mentioned (few events generated in the SHERPA sample and the inefficiency introduced by the PR tool), an integrated value calculated in SR-A with a softer meff cut (500 GeV) was used for all the TFs. The values obtained are shown in Figure C.15. Even so, using PR has an effect on this value as shown by Table C.14, although this is smaller than the overall assigned uncertainty quoted in Table C.13. The results were again cross-checked with SMDP results in [116] by resolving the different components: Aγ · εγ = Aγ · εγrec · εγid. For εγrec, the SMDP result for photons with average pT shown in Table 5.16 was estimated to be ∼ 83%± 1% and for εγid ∼ 94%± 1%. The Aγ was estimated from photon MC passing only the 0` selection and bypassing the γ +X selection using truth photon information and the result 216 Results from Previous Analyses obtained was practically identical to that shown in Table 5.17. Estimated this way, the value of Aγ · εγ was compared to that in Figure C.15 and their difference taken as the final uncertainty, shown in Table C.13 (row 3). • Purity: Given the high and robust purity of the CR1a sample (Section 5.5.2), the remaining background was like in Moriond’11, neglected, and rather an uncertainity of 3% assigned to it, based on the maximum background estimate in [116] within the approximate photon pT range of the CR1a candidates, as shown in Table C.13 (row 2). • Z/γ Ratio: The value was again taken from GAMBOS but as an improvement with respect to the previous analysis, this time the variations with jet multiplicity, reconstruction effects and isolation criteria (Chapter 4 and Section 5.5.3) were at least considered this time by assigning a more conservative uncertainty of 15%, as shown in Table C.13 (row 8), given that the effects from PDFs largely cancel (a < 5% effect). • γ vs Zνν Pseudorapidity: Given that the γ and Zνν η distributions are effectively identical in the SRs (e.g. Figures 5.15 and 4.14(b)), the difference found between γ + jets and Zνν + jets MC was taken as the uncertainty, as shown in Table C.13 (row 4). Other uncertainties that were assessed to be consistent with the rest of the 0` analysis, also appearing in Table C.13, were: • Pileup: This was obtained from the difference of using “BCID non-averaged reweigh- ing” and the default (BCID averaged) in the PR tool. • JES/JER: Jet energy scale and jet energy resolution uncertainties were assessed using the standard ATLAS tools provided by the Jet/ETmiss working group available at the time. More details can be found in [102]. • Trigger: This was with respect to the nearly 100% efficient photon trigger used in this analysis (g60 loose, see Appendix B). Results from Previous Analyses 217 Figure C.15.: PLHC’11 Combined acceptance and efficiency correction factor Aγ(pT) · εγ(pT) for the CR1a TF in SR-A with softer meff cut (500 GeV), as obtained from γ + jets SHERPA. Signal Region 〈Aγ(pT) · εγ(pT)〉 no PR PR A 0.93 0.99 B 0.78 0.78 C 0.77 0.69 D 0.90 0.61 E 0.67 0.00 Table C.14.: PLHC’11 Effect of using the pileup reweighing tool on the integrated value of Aγ(pT) · εγ(pT) in the SRs (Figure C.15). 218 Results from Previous Analyses TF stand-alone estimate of Zνν + jets: After the direct application of the TF to the CR1a event counts, the Zνν + jets background estimate results obtained for this analysis are shown in Table C.15 compared to SHERPA and ALPGEN, where all the results are consistent within errors. Two examples to illustrate these results are shown in Figure C.16 for SR-A with softer meff cut and SR-C. The data-MC agreement is clearly best for the bin with the largest statistics, and the Zνν + jets ALPGEN sample describes better the data estimate in Figure C.16. SR CR1a Zνν + jets Estimate Zνν + jets Signal data Sherpa data Sherpa Sherpa/Alpgen A 15 21 5.6 ± 1.5 (stat) ± 1.5 (syst) 8.4 3.5/6.0 B 12 15 4.5 ± 1.3 (stat) ± 1.1 (syst) 5.9 2.0/5.0 C 127 108 38.7 ± 3.4 (stat) ± 7.6 (syst) 35.3 30.9/34.3 D 8 6 3.0 ± 1.1 (stat) ± 0.8 (syst) 2.5 1.3/1.7 E 3 0 1.0 ± 0.6 (stat) ± 0.4 (syst) 0 0.4/0.4 Table C.15.: PLHC’11 numbers of CR1a events from data and MC for each SR (columns 2-3) and the stand-alone estimate of Zνν + jets background in the SRs from data and MC (columns 4-5), compared to Zνν + jets MC (column 6). The MC statistical uncertainty is not shown but can be assumed to be small. The luminosity uncertainty was then ∼ 4.5% (Table 5.2). [GeV]effM 0 500 1000 1500 2000 2500 3000 En tri es / 10 0. 0 G eV 1 10 210 310 +jets Sherpa Estimateγ Data 2011 Estimate +jets Sherpaνν Z +jets Alpgenνν Z -1L dt ~165 pb∫ Dijet channel (a) [GeV]effM 0 500 1000 1500 2000 2500 3000 En tri es / 10 0. 0 G eV -110 1 10 210 310 +jets Sherpa Estimateγ Data 2011 Estimate +jets Sherpaνν Z +jets Alpgenνν Z -1L dt ~165 pb∫ Four Jet channel (b) Figure C.16.: PLHC’11 Zνν + jets meff distributions in the 0` (a) SR-A with softer meff cut (500 GeV) and (b) SR-C, as estimated from CR1a from data and MC using the TF, compared directly with Zνν + jets MC from SHERPA and ALPGEN. The labels ‘Data 2011 Estimate’ and ‘γ+ jets Sherpa estimate’ indicate the TFs were applied to the CR1a data or MC events, whereas those labeled ‘Zνν + jets Sherpa/Alpgen’ show the raw MC Zνν + jets estimates for the SRs scaled to the data luminosity. Results from Previous Analyses 219 C.2.6. Context within the 0` analysis The 0` SRs meff distributions (prior to the meff cut) are shown in Figure C.17, together with the ‘raw’ MC background expectations prior to the likelihood fitting procedure. The equivalent distributions for the CRs can be found in [102]. The corresponding event counts in the SRs and CRs are listed in Table C.16, where once again the rich statistics of CR1a become evident. SR-C was clearly the region with the largest statistics. The central values of the TFs used to translate the CR event counts into SR background estimates are quoted in Table C.17, featuring again the robustness of the CR1a TF accross all SRs (see Section 5.6.2). Tables like Table 5.24 which list the cross-TFs (Section 5.6.1) are not shown here but can be found in [102]. At the time of PLHC’11, there was no defined procedure to include both CR1a and CR1b into the same likelihood fit (unlike in the current implementation, see Section 5.6.1), so two different fits were done; one using CR1a and one using CR1b, shown in Tables C.19 and C.20 respectively, from which both estimates were considered consistent in SR-A, B and D, but not in SR-C (a ∼ 2σ discrepancy). However, despite SR-C being the SR with largest statistics, CR1b showed significantly larger uncertainties compared to the other CRs, as shown in Table C.18 (probably as a result of the CR1b-to-SR extrapolation) and also the corresponding TF central value was significantly different with respect to the others (see Table C.17). Another problem encountered was that the hardest SR, SR-E, showed too large statistical uncertainties for the likelihood fit to provide reliable results. Because of this, both of SR-C and SR-E were excluded from the final 0` results presented at the PLHC’11 conference [65] and only CR1a was considered to estimate the Zνν + jets background estimate (hence it is referred in [65] simply as ‘CR1’). This demonstrated the importance of the Zνν + jets background estimate in the 0` analysis. Given that no significant excess was found between the data and SM expectation, limits were set on the same SUSY models as in Moriond’11, shown in Figure C.18. Under these models, the gluino mass was excluded below 725 and up to 1025 GeV, while equal mass squarks and gluinos were excluded below 950 GeV. The larger jet multiplicities and harder selections of the PLHC’11 SRs improved the reach with respect to the Moriond’11 analysis. 220 Results from Previous Analyses En tri es / 10 0 G eV 1 10 210 310 410 510 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt ~ 165 pb∫ Dijet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A / M C -0.5 0 0.5 1 1.5 2 2.5 D AT A / M C En tri es / 10 0 G eV -110 1 10 210 310 410 510 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt ~ 165 pb∫ Three Jet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A / M C -0.5 0 0.5 1 1.5 2 2.5 D AT A / M C En tri es / 10 0 G eV -110 1 10 210 310 410 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt ~ 165 pb∫ Four Jet Channel ATLAS Preliminary Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A / M C -0.5 0 0.5 1 1.5 2 2.5 D AT A / M C Figure C.17.: PLHC’11 meff distributions for the ≥ 2 jet channel (top left), the ≥ 3 jet channel (top right) and the ≥ 4 jet channel (bottom), prior to the meff cut (red arrows indicate the start of a SR), in data and MC. For comparison, the dashed curve shows the expectation for an mSUGRA reference point with m0 = 660 GeV, m1/2 = 240 GeV, A0 = 0, tanβ = 10 and µ > 0. This reference point is also indicated by the star on Figure C.18(b). Below each plot the data/MC ratio is shown. Black vertical bars show the statistical uncertainty from the data, while the yellow band shows the size of the combined SM MC statistical, JER and JES uncertainties. From [65]. Results from Previous Analyses 221 Region Channel A B C D E SR 10 8 198 7 4 CR1a 15 12 127 8 3 CR1b 11 10 7 4 2 CR2 8 17 122 8 10 CR3 74 67 44 51 13 CR4 9 17 24 23 10 Table C.16.: PLHC’11 data event counts in the 0` SRs and CRs. From [102]. Control region / process Signal Region A B C D E CR 1a / Z(→ νν)+jets 0.38 0.37 0.3 0.37 0.34 CR 1b / Z(→ νν)+jets 0.65 0.65 12 0.66 0.0001 CR 2 / QCD jets 0.014 0.017 0.13 0.036 0.049 CR 3 / W (→ `ν)+jets 0.09 0.081 2.1 0.075 0.085 CR 4 / tt¯ 0.048 0.075 4.2 0.07 0.082 Table C.17.: PLHC’11 Summary of the central values of the CRs TFs in every channel. From [102]. 222 Results from Previous Analyses Uncertainty Process (main CR) Z+jets (CR1a) Z+jets (CR1b) QCD jets (CR2) W+jets (CR3) tt¯ (CR4) Central Value 0.3 12 0.13 2.1 4.2 JES +0−2.2 % +20 −1.7 % – +3.3 −2.5 % +5.9 −5.4 % JER 1.4 % 11 % – 2 % 4.1 % CR bckgrnd. 3 % – – – – γ acceptance. 7 % – – – – γ → Z acc. corr. 2 % – – – – Trigger < 1 % – – – – QCD seed – – 9.2 % – – QCD Gaussian – – 23 % – – QCD tail norm. – – 4.6 % – – QCD tail stat. – – 11 % – – l eff. – 7.1 % – 2.5 % 2.2 % l scale. – 16 % – 1.2 % 1.5 % l resoln. – 1.9 % – 0.77 % 0.45 % b-tag/veto eff. – – – 18 % 26 % Theory 15 % 32 % – 17 % 15 % Pileup 4 % – – 1.4 % 5.3 % MET CellOut – – – 1.8 % 1.9 % MC stat. – 4.2 % – 5.9 % 8.2 % Table C.18.: PLHC’11 uncertainties of the CRs TFs to SR-C (the SR with largest statistics). CR1b has significantly larger uncertainties and central value compared to the other CRs. From [102]. Process Signal Region A B C D E CR1a / Z → (νν)+jets 5.61± 2.11 4.44± 1.6 38.55± 7.58 2.96± 1.33 0.01± 0.0 W → (`ν)+jets 6.2± 1.81 4.45± 1.59 57.43± 31.09 2.73± 1.3 0.0± 1.11 tt¯+ Single Top 0.22± 0.33 1.01± 0.92 89.51± 37.53 1.41± 0.89 1.36± 0.55 QCD jets 0.05± 0.04 0.21± 0.07 12.28± 1.56 0.16± 0.11 0.0± 0.29 Total 12.08± 2.77 10.1± 2.34 197.77± 27.05 7.27± 1.71 1.37± 1.23 Data 10 8 198 7 4 Table C.19.: PLHC’11 Fitted background components in each SR, compared with observation using CR1a. The Z+ jets and W + jets are for most SRs the dominant backgrounds. From [102]. Results from Previous Analyses 223 Process Signal Region A B C D E CR1a / Z → (νν)+jets 7.1± 2.14 6.48± 2.07 82.69± 20.84 2.65± 1.43 0.0± 0.29 W → (`ν)+jets 6.17± 1.49 4.4± 1.13 57.46± 15.1 2.72± 0.79 0.67± 0.38 tt¯+ Single Top 0.22± 0.26 1.0± 0.67 89.06± 16.27 1.41± 0.55 0.74± 0.29 QCD jets 0.05± 0.04 0.2± 0.07 11.48± 1.48 0.17± 0.1 0.67± 0.21 Total 13.55± 3.66 12.08± 3.72 240.69± 52.01 6.95± 2.08 2.08± 0.62 Data 10 8 198 7 4 Table C.20.: PLHC’11 Fitted background components in each SR, compared with observation using CR1b. The Z+ jets and W + jets are for most SRs the dominant backgrounds. From [102]. gluino mass [GeV] 0 250 500 750 1000 1250 1500 1750 2000 sq ua rk m as s [G eV ] 0 250 500 750 1000 1250 1500 1750 2000 = 10 pbSUSYσ = 1 pbSUSYσ = 0.1 pbSUSYσ ) 1 0χ∼Squark-gluino-neutralino model (massless =7 TeVs, -1 = 165 pbintL 0 lepton 2011 combined PreliminaryATLAS q~LEP 2 Tevatron, Run I D0, Run II CDF, Run II }CMSSMMSUGRA / Observed 95% C.L. limit Median expected limit Observed 95% C.L. limitsCL Median expected limitsCL 2010 data PCL 95% C.L. limit [GeV]0m 500 1000 1500 2000 2500 [G eV ] 1/ 2 m 150 200 250 300 350 400 450 500 550 600 (600)g~ (800)g~ (1000)g~ (600) q~ (1000) q~ (1400) q ~ >0µ= 0, 0 = 10, AβMSUGRA/CMSSM: tan =7 TeVs, -1 = 165 pbintL 0 lepton 2011 combined PreliminaryATLAS 1 ± χ∼LEP 2 -1<0, 2.1 fbµ=3, β, tanq~, g~D0 -1<0, 2 fbµ=5, β, tanq~,g~CDF Observed 95% C.L. limit Median expected limit Observed 95 % C.L. limitsCL Median expected limit sCL Reference point 2010 data PCL 95% C.L. limit CMS 2010 Razor,Jets/MHT Figure C.18.: PLHC’11 95% CLs exclusion limits obtained by using the SR with the best expected sensitivity at each point in (a) a simplified MSSM scenario with only strong production of gluinos and first- and second-generation squarks, and direct decays to jets and neutralinos; and in (b) the (m0 ; m1/2) plane of MSUGRA/CMSSM for tanβ = 10, A0 = 0 and µ > 0 (right). The red lines show the observed limits, the dashed-blue lines the median expected limits, and the dotted blue lines the ±1σ variation on the expected limits. Comparison with previous limits is illustrative only as some are derived in a different context. From [58]. 224 Results from Previous Analyses C.3. EPS’11 (1.04 fb−1) The results from this analysis round became the second publication of the 0` analysis [54]. The corresponding ZfromGamma results are documented in the supporting 0` documenta- tion, found in [101]. Given the short time scale between EPS’11 and the previous analysis round (PLHC’11), not many improvements could be made to the ZfromGamma method, except for making used of two additional γ + jets SHERPA samples, which in the end turned out still insufficient for the harder SRs of EPS’11. As for 0` analysis itself, the main changes with respect to PLHC’11 were: • A significantly larger dataset (by almost an order of magnitude). • A ‘LAr hole’ – a region in the ATLAS LAr calorimeter (0 < η < 1.4 and −0.8 < φ < −0.6) that had a major electronics failure from data-period E onwards. In summary, the impact on the 0` analysis from this was: for jets, the reconstruction was negligibly affected if the jet pT was > 20 GeV but the mean energy loss was still ∼ 30%; for EmissT , both the scale and resolution were affected; for the CRs, the impact was negligible except for CR2 (QCD) given that substantial fake EmissT could be generated by jets pointing into the hole. In addition, the γ + jets events which were never a worry to the 0` analysis as none were expected to pass to the SRs (little true EmissT is expect from such events, see Appendix D.2), became a concern. Similar to CR2, a high-pT photon pointing into the hole could significantly contribute to the measured EmissT and so, such event could potentially pass to the SRs. This was another case for which the ZfromGamma method proved useful and luckily the effect was found to be negligible, as described in Appendix D.2.1. In order to counteract all these effects, a ‘LAr hole veto’ was defined (and regarded as an ‘event cleaning cut’), where the event was rejected if any of the leading-four jets had pT > 30 GeV and pointed into the hole. The impact of the LAr hole veto on the CRs was found to be negligible [101] and the overall decrease in SUSY signal acceptance to be no more than 15%. • The incorporation of SR-C and E (Table C.11), which had been excluded in PLHC’11 to obtain the final limit plots. • A procedure to incorporate both CR1a and CR1b into the likelihood fit to obtain a combined and more robust Zνν + jets background estimate. Results from Previous Analyses 225 • The use of “validation regions” (VRs) to cross-check CR3 (W`ν + jets) and CR4 (tt¯) and the removal of the theory uncertainties associated with the extrapolation in these CRs by applying the same meff cut as in the SRs (though the extrapolation in CR1b remained). • Additional SUSY interpretations of the results, e.g. in Universal Extra Dimensions (UED) models [118]. C.3.1. Framework The framework used in this analysis is specified in Section 5.1 and Table 5.1. C.3.2. Event Samples Data: The data was in SUSYD3PD format and included 2011 data periods B2-H4, amounting to ∫ L dt ∼ 1.035 fb−1 after applying the EPS’11 0` GRL (more details in Table 5.2). Monte Carlo: The MC samples used in this analysis are listed in Tables C.21-C.22 and the production details in Table 5.7. The γ + jets PYTHIA sample from Table C.9 was no longer used because of the already known missing multijet events (Sections C.1.4 and C.2.4). The new highlight was the availability of a higher-pT γ + jets SHERPA sample (referred to here as ‘SHERPA-140’). However, as will be shown in Section C.3.4, this proved still insufficient for the EPS’11 SRs. Again, background samples to the γ + jets signal were not included in the plots given the high-purity of the photon sample and time constrains to produce these samples (this issue was sorted for Moriond’12). As for Zνν + jets MC, the same SHERPA and ALPGEN samples as in PLHC’11 (albeit under different production settings, see Table 5.7) were used. Regarding matching data-conditions, the MC production for EPS’11 (‘mc10b’ in Table 5.7) had more refined settings to match the pileup conditions than the PLHC’11 production (‘mc10a’). The typical distribution of the number of interactions per event is shown in Figure C.19 for the γ + jets SHERPA-70 sample. However, it was not until Moriond’12 when the MC production was truly suited for 2011 data (‘mc11’), as both EPS’11 and PLHC’11’s production had been based on 2010 data with an added pileup component. 226 Results from Previous Analyses In all the plots that follow, the MC is normalised to the data luminosity using the cross-sections listed and the same pileup reweighing tool from PLHC’11 was implemented (see Section C.2.2). Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 113715 SherpaY4JetsPt70 1.5634 · 10+3 1.000 1.000 199930 113716 SherpaY4JetsPt140 9.7628 · 10+1 1.000 1.000 199849 Table C.21.: EPS’11 Monte Carlo samples to simulate the γ + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. Sample ID Name Cross Section [pb] Filter Eff. k-factor Ngen 119932 Z5jetstonunu30GeVScaleMT 5.2941 · 10+3 1.0 1.000 1699681 107710 AlpgenJimmyZnunuNp0 pt20 filt1jet 3.572 · 10+3 0.011 1.282 63482 107711 AlpgenJimmyZnunuNp1 pt20 filt1jet 7.387 · 10+2 0.611 1.282 909288 107712 AlpgenJimmyZnunuNp2 pt20 filt1jet 2.229 · 10+2 0.882 1.282 204942 107713 AlpgenJimmyZnunuNp3 pt20 filt1jet 6.187 · 10+1 0.968 1.282 140929 107714 AlpgenJimmyZnunuNp4 pt20 filt1jet 1.563 · 10+1 0.992 1.282 32980 107715 AlpgenJimmyZnunuNp5 pt20 filt1jet 3.581 · 10+0 0.998 1.282 9492 Table C.22.: EPS’11 Monte Carlo samples to simulate the Zνν + jets signal, including cross section times filter efficiency, k-factor and the number of generated events in the sample. htemp Entries 9995 Mean 8.575 RMS 3.08 lbn 2 4 6 8 10 12 14 160 200 400 600 800 1000 1200 lbn Figure C.19.: EPS’11 Distribution of 〈µ〉 in the γ + jets SHERPA-70 sample, to illustrate the MC production settings of the ‘mc10b’ to match the EPS’11 data conditions. The mean of 〈µ〉 is indeed ∼ 8, as quoted in Table 5.7. Results from Previous Analyses 227 C.3.3. Inclusive Photon Sample (γ +X) Event Selection: A slightly updated version of the photon selection with respect to the SMDP 35 pb−1 analysis [49] was implemented here, mainly to deal with the LAr hole problem discussed, as well as the new lowest unprescaled photon-trigger suitable for the EPS’11 dataset. The requirements are shown in Tables 5.8 and 5.9, which were largely based on the SMDP recommendations at the time [87]. Technically, the main changes were: an update of the ‘photon cleaning’ also related to the LAr hole (see Section 5.3.1); a higher photon-pT cut (to suit the trigger); a harder PV requirement and the addition of a LAr error check. Results: The results for the γ +X selection just described were also presented at the EPS’11 conference as a separate analysis documented in [92]. The pT distribution for the prompt photon candidates is shown in Figure C.20 for two isolation criteria; the one used in Table 5.8 and the then ‘test’ looser criteria of EisoT < 5 GeV. This was because the criterion used in the 880 nb−1 and 35 pb−1 SMDP analyses had been motivated by the lower photon-pT acceptance and the consequently larger background contamination. However, for Moriond’12 onwards, EisoT < 5 GeV became the default criterion (note that the integrated luminosity of Figure C.20 is slightly lower than in the 0` analysis because the EPS’11 SMDP GRL was used to obtain these plots). With the SMDP GRL, the number of prompt photon candidates was 529 481 with 3 GeV isolation and 628 497 with 5 GeV isolation. For Figure C.20(b), 5 candidates were found with pT > 800 GeV (4 unconverted, 1 converted); the highest-pT unconverted photon had pT ∼ 960 GeV and its event display is shown in Figure C.21. The equivalent distribution to Figure C.20(a) but using the 0` GRL is shown in Figure C.22 and the cutflow quoted in Table 5.10, which was found to be in very good agreement with the SMDP results in [92]. C.3.4. Control Region Sample (CR1a) 0` selection: Having applied the CR1a object definitions (Section 5.4) and 0` object definitions in [101], the discriminant 0` event selections were identical to PLHC’11 (Table C.11). The detailed version, e.g. with the updated cleaning cuts, can be found in [101]. 228 Results from Previous Analyses [GeV]TE 100 200 300 400 500 600 700 800 900 1000 [1/ Ge V] T 1/ N dN /d E -810 -710 -610 -510 -410 -310 -210 -110 ATLAS Internal Only -1 Ldt = 1.08 fb∫= 7 TeV, s )γData 2011 (tight, isolated < 3 GeVisoTE (a) [GeV]TE 100 200 300 400 500 600 700 800 900 1000 [1/ Ge V] T 1/ N dN /d E -810 -710 -610 -510 -410 -310 -210 -110 ATLAS Preliminary -1 Ldt = 1.08 fb∫= 7 TeV, s )γData 2011 (tight, isolated < 5 GeVisoTE (b) Figure C.20.: EPS’11 pT distribution of the prompt photon candidates in the γ +X sample from data, using two different isolation criteria: (a) the one used up to the EPS’11 analysis (EisoT < 3 GeV) and (b) a looser criterion used in Moriond’12 (E iso T < 5 GeV). The bins are of variable size and normalised to the total number of selected candidates. The marker positions correspond to the bin weighted averages. The integrated luminosity is slightly lower than in the 0` analysis because the EPS’11 SMDP GRL was used for these plots. From [92]. Results: For this part, some relevant results have been discussed in Section 5.4. Fig- ure C.22 shows the prompt photon pT evolution from the γ +X selection to the CR1a selection for SR-A in data and the SHERPA-70 signal. To get the MC CR1a meff distributions, the original plan was to continue using the SHERPA-70 sample, which had been used to produce for example Figure C.22. With this, the resulting meff distributions for all SRs are shown in Figure C.23 (prior to the meff cut). However, a significant data-MC discrepancy was found in the distribution for SR-C/D, as shown in Figure C.23(c). This issue was investigated further and found to be due to the pileup reweighing tool introducing a loss in statistics (see Appendix C.2.4). To support such conjecture, Figure C.24 shows the equivalent of Figure C.23 but without PR applied, and clearly the effect is negligible for all SRs except for SR-C/D, where a significant improvement in the data/MC agreement results. However, because the ultimate aim was to be as consistent as possible with the 0` analysis, another solution was sought after to avoid not using this tool. For this, the SHERPA-140 sample with PR applied was investigated and, although it was found to be in good agreement with data at high-meff , it was discrepant at low-meff . Further investigation of this issue showed that there were missing low-pT photon events in SHERPA-140 that could pass the SRs selections. This is illustrated in Figure C.25 where the meff distribution for SR-C/D is plotted versus pT(γ1) for both SHERPA-140 and SHERPA-70, from which is clear that SHERPA-70 events with photons of pT lower than the generator-level cut of SHERPA-140 can certainly pass Results from Previous Analyses 229 Figure C.21.: EPS’11 Event display of event 15829585 in run 183407, showing the highest-pT unconverted prompt photon candidate in the dataset using the SMDP GRL. The candidate has reconstructed pT = 960 GeV and impacts at η = 0.35, φ = 2.44. It has E iso T = −562 MeV. The main balancing jet has reconstructed pT = 918 GeVand impacts at η = -0.48, φ = -0.45; the event has reconstructed EmissT = 22.5 GeV. The event display shows tracks with pT > 2 GeV. 230 Results from Previous Analyses ph_pt [GeV] 0 100 200 300 400 500 600 700 800 900 1000 Ev en ts / 20 G eV 1 10 210 310 410 510 610 +jets Sherpa70γ =7 TeV)sData 2011 ( -1L dt ~1035 pb∫ (a) J2CR_ph_pt [GeV] 0 100 200 300 400 500 600 700 800 900 1000 Ev en ts / 40 G eV 1 10 210 310 410 +jets Sherpa70γ =7 TeV)sData 2011 ( -1L dt ~1035 pb∫ Dijet channel (b) Figure C.22.: EPS’11 prompt photon pT distribution in data and MC at different stages of the CR1a selection: (a) after the γ +X selection and (b) after the CR1a selection for SR-A with a softer meff cut (500 GeV). The MC shown is the SHERPA-70 signal. Figure (a) is the equivalent of Figure C.20(a) but using the 0` GRL. the SR-C/D selection (although the magnitude of the effect is misrepresented by the poor statistics of the SHERPA-70 sample). As additional evidence of this effect, Figure C.26 shows the CR1a pT(γ1) distribution for SR-C in SHERPA-70 and SHERPA-140 – clearly the lower pT bins in SHERPA-140 have some events that are missing in SHERPA 70. In the end, the final consensus for the 0` publication was to use SHERPA-140 for all CR1a meff plots with a scaling factor/correction applied at low meff and obtained from SHERPA-70. The result is shown in Figure C.27 and the scaling factors applied are listed in Table C.23. The number of events in these plots is shown in Table C.25 for both data and MC (columns 2 and 3) and the corresponding average pT(γ1) and range are quoted in Table 5.16. SR meff Range [GeV] < 300 300 - 400 400 - 500 500 - 600 600 - 700 > 700 A n/a 1.7747 1.1912 1.0 1.0 1.0 B n/a 2.1003 1.3702 1.4215 1.0 1.0 C/D n/a 1.6130 1.4007 1.0 1.0 1.0 E n/a n/a n/a n/a n/a 1.0 Table C.23.: EPS’11 Scaling factors applied on the SHERPA-140 CR1a meff distributions, obtained from the SHERPA-70 sample. The ‘n/a’ means the corresponding meff range had zero bin entries. Results from Previous Analyses 231 En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Dijet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (a) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Three Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (b) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Four Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 3 3.5 (c) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Four Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (d) Figure C.23.: EPS’11 CR1a meff distributions in data and MC for SR (a) A, (b) B, (c) C/D and (d) E. The MC shown is the SHERPA-70 with pileup reweighing applied. The yellow band in the data/MC ratio denotes the size of the combined JER/JES and MC statistical uncertainties. 232 Results from Previous Analyses En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Dijet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (a) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Three Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (b) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Four Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 3 3.5 (c) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jets Sherpaγ -1L dt ~1.04 fb∫ Four Jet High Mass Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 D AT A/ M C -0.5 0 0.5 1 1.5 2 2.5 (d) Figure C.24.: EPS’11 CR1a meff distributions in data and MC for SR (a) A, (b) B, (c) C/D and (d) E. The MC shown is the SHERPA-70 without pileup reweighing applied. The yellow band in the data/MC ratio denotes the size of the combined JER/JES and MC statistical uncertainties. Results from Previous Analyses 233 0 50 100 150 200 250 3000 200 400 600 800 1000 1200 1400 J4METdPhiRatCD_meff_vs_ph_pt Entries 1045 Mean x 207.7 Mean y 622.9 RMS x 44.22 RMS y 121.6 0 0.001 0.002 0.003 0.004 0.005 J4METdPhiRatCD_meff_vs_ph_pt (a) 0 50 100 150 200 2500 200 400 600 800 1000 1200 J4METdPhiRatCD_meff_vs_ph_pt Entries 72 Mean x 182 Mean y 613.1 RMS x 51.97 RMS y 114.8 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 J4METdPhiRatCD_meff_vs_ph_pt (b) Figure C.25.: EPS’11 CR1a meff vs pT(γ1) distributions in MC for SR-C/D prior to the meff cut. The MC shown is (a) SHERPA-70 without PR and (b) SHERPA-140 without PR. Note the statistics of the SHERPA-70 in are very limited (see Table C.21). 0 100 200 300 400 500 600 700 800 900 -310 -210 -110 70reco 70truth 140truth 140reco Figure C.26.: EPS’11 true and reconstructed prompt photon pT distribution in SR-C in SHERPA-70 and SHERPA-140. Both samples are normalised to the cross-section only. 234 Results from Previous Analyses En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jetsγ -1L dt = 1.04 fb∫ ATLAS Dijet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 DA TA /M C 0 0.5 1 1.5 2 2.5 (a) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jetsγ -1L dt = 1.04 fb∫ ATLAS Three Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 DA TA /M C 0 0.5 1 1.5 2 2.5 (b) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jetsγ -1L dt = 1.04 fb∫ ATLAS Four Jet Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 DA TA /M C 0 0.5 1 1.5 2 2.5 (c) En tri es / 10 0 G eV 1 10 210 310 410 50 610 =7 TeV)sData 2011 ( +jetsγ -1L dt = 1.04 fb∫ ATLAS Four Jet High Mass Channel Meff [GeV] 0 500 1000 1500 2000 2500 3000 DA TA /M C 0 0.5 1 1.5 2 2.5 (d) Figure C.27.: EPS’11 final CR1a meff distributions in data and MC for SR (a) A, (b) B, (c) C/D and (d) E. The MC shown is the SHERPA-140 signal scaled by the SHERPA-70 signal at low meff by the factors in Table C.23. The yellow band in the data/MC ratio denotes the size of the combined JER/JES and MC statistical uncertainties and includes the error on the scaling factor. Results from Previous Analyses 235 C.3.5. Transfer Function (TFZνν) As mentioned, given the short time scale between PLHC’11 and EPS’11, it was not possible to further improve the calculation of the CR1a TFs with respect to what was done for PLHC’11. The TF central values and associated uncertainties obtained are shown in Table C.24 and a summary of the procedures to calculate each of the factors now follows. Uncertainty TF Zνν Est. from γ + jets A B C D E Central Value 0.376 0.382 0.339 0.39 0.34 CR bckgrnd. (fbkg) 5% 5% 5% 5% 5% Aγ · εγ 4.5% 5.0% 4.6% 6.5% 14.3% ηZ/γ 2% 2% 2% 2% 2% JES/JER +6.4%−8.2% +8.5% −7.5% +1.2% −2.9% +4.3% −1.3% +0% −0% Pileup (A× ε) 0.3% 1.1% 0.3% 1.3% 1.9% Trigger < 1% < 1% < 1% < 1% < 1% Theory (RZνν/γ) 15% 15% 15% 15% 15% Table C.24.: EPS’11 Central values and associated uncertainties of the CR1a TFs in the PLHC’11 analysis. The meaning of the terms are explained elsewhere in the text. • Efficiency and Acceptance: The same procedure as in PLHC’11 was followed. • Purity: The same procedure as in PLHC’11 was followed (see Section C.2.5), except that the uncertainty assigned was increased from ∼ 3% to ∼ 5% to include the effects of electrons in W + jets decays misidentified as photons. The SMDP group had estimated this background to be around 1% for the photon-pT range considered here [99]. • Z/γ Ratio: The same procedure as in PLHC’11 was followed. • γ vs Zνν Pseudorapidity: The same procedure as in PLHC’11 was followed. Other uncertainties that were assessed to be consistent with the rest of the 0` analysis, also appearing in Table C.24, were: • Pileup: The same procedure as in PLHC’11 was followed. 236 Results from Previous Analyses • JES/JER: The same procedure as in PLHC’11 was followed. • Trigger: This was with respect to the nearly 100% efficient photon trigger used (g80 loose, see Appendix B). TF stand-alone estimate of Zνν+jets: After the application of the TF to the CR1a event counts, the Zνν + jets background estimate results obtained for this analysis are shown in Table C.25 compared to SHERPA and ALPGEN, where all the results are consistent within errors. Two examples to illustrate these results are shown in Figure C.28 for SR-A with softer meff cut and SR-C. Note that the Zνν + jets ALPGEN prediction includes a k-factors of 1.282 (see Table C.22) while the SHERPA equivalent does not, although this does not affect the data-driven CR1a estimate. SR CR1a Zνν + jets Estimate Zνν + jets Signal data Sherpa data Sherpa Sherpa/Alpgen A 76 94 28.6 ± 3.3 (stat) ± 5.3 (syst) 38.9 16.6/36.3 B 59 54 22.6 ± 2.9 (stat) ± 4.2 (syst) 22.0 20.7/36.5 C 572 417 194.0 ± 8.1 (stat) ± 32.7 (syst) 158.5 181.2/235.7 D 35 34 13.7 ± 2.3 (stat) ± 2.4 (syst) 14.2 2.8/18.1 E 8 9 2.7 ± 1.0 (stat) ± 0.6 (syst) 3.5 4.0/4.0 Table C.25.: EPS’11 numbers of CR1a events from data and MC for each SR (columns 2-3) and the stand-alone estimate of Zνν + jets background in the SRs from data and MC (columns 4-5), compared to Zνν + jets MC (column 6). The luminosity uncertainty was then ∼ 4.5% (Table 5.2). C.3.6. Context within the 0` analysis The 0` SRs meff distributions (prior to the meff cut) are shown in Figure C.29 for data and the ‘raw’ MC background expectations (prior to the likelihood fitting procedure). Numerically, these distributions are represented by the SR event counts in Table C.26 (row 1) and the MC background expectations in Table C.27. The equivalent distributions for the CRs can be found in [101] and the respective event counts listed in Table C.26. The TFs central values used to translate the CR event counts into SR background estimates are presented in Table C.28. The version of Table C.28 actually fed into the likelihood fit is in the form of ‘cross-TFs’ (see Section 5.6.1), which takes into account Results from Previous Analyses 237 [GeV]effM 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 310 +jets Sherpa140 Estimateγ Data 2011 Estimate +jets Sherpaνν Z +jets Alpgenνν Z -1L dt ~1035 pb∫ Dijet channel (a) [GeV]effM 0 500 1000 1500 2000 2500 3000 En tri es / 10 0 G eV 1 10 210 +jets Sherpa140 Estimateγ Data 2011 Estimate +jets Sherpaνν Z +jets Alpgenνν Z -1L dt ~1035 pb∫ Four Jet channel (b) Figure C.28.: EPS’11 Zνν + jets meff distribution as estimated from CR1a, directly compared to Zνν + jets MC from SHERPA and ALPGEN for: (a) SR-A with softer meff cut (500 GeV) and (b) SR-C. correlations, mutual contamination, as well as the small correction to the CR1a TF from the additional background contribution arising from Z decays to misidentified charged leptons (see also Section 5.6.1). An example of this is shown in Table C.29 for SR-E and the rest can be found in [101]. In all these plots and numbers, the same features registered in PLHC’11 for CR1a were observed (large statistics, TF robustness and large contribution to the total SM expectation, see Section C.2.6), simply scaled by the EPS’11 increase in data luminosity when relevant. Region Channel A B C D E SR 58 59 1118 40 18 CR1a 76 59 572 35 8 CR1b 91 59 31 29 7 CR2 57 97 762 41 34 CR3 70 84 249 58 15 CR4 11 19 142 19 12 Table C.26.: EPS’11 data event counts in the 0` SRs and CRs. From [101]. 238 Results from Previous Analyses En tri es / 10 0 G eV 1 10 210 310 410 510 610 = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt = 1.04 fb∫ Dijet Channel ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / M C 0 0.5 1 1.5 2 2.5 En tri es / 10 0 G eV 1 10 210 310 410 510 = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt = 1.04 fb∫ Three Jet Channel ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / M C 0 0.5 1 1.5 2 2.5 En tri es / 10 0 G eV 1 10 210 310 410 510 = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt = 1.04 fb∫ Four Jet Channel ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / M C 0 0.5 1 1.5 2 2.5 En tri es / 15 0 G eV -110 1 10 210 310 410 510 = 7 TeV)sData 2011 ( SM Total QCD multijet W+jets Z+jets and single toptt SM + SU(660,240,0,10) -1L dt = 1.04 fb∫ Four Jet High Mass Channel ATLAS [GeV] effm 0 500 1000 1500 2000 2500 3000 DA TA / M C 0 0.5 1 1.5 2 2.5 Figure C.29.: EPS’11 meff distributions for SR A (top), B (top right), C/D (bottom left) and E (bottom right) prior to the meff cut in data, SM MC (the samples used are specified in [101]) and a mSUGRA reference point with m0 = 660 GeV, m1/2 = 240 GeV, A0 = 0, tanβ = 10 and µ > 0 (this point is also indicated by the star on Figure C.30(b)). Red arrows mark the start of the SRs. Below each plot the ratio of the data to the SM expectation is provided. Black vertical bars show the statistical uncertainty from the data, while the yellow band shows the size of the systematic uncertainties from the MC simulation. From [54]. Results from Previous Analyses 239 SM process Signal Region A B C D E Z+jets 36.6 37.6 245 18.8 4.28 W+jets 28.3 27 406 13.5 3.85 tt¯ + Single Top 2.74 4.54 417 5.42 5.95 QCD jets 0.00177 0.00431 17.5 0.129 0.171 Total SM 67.6 69.1 1.09e+03 37.9 14.2 Table C.27.: EPS’11 Summary of the MC expectations of each background component for all SRs. From [101]. Control region / process Signal Region A B C D E CR 1a / Z(→ νν)+jets 0.38 0.38 0.34 0.39 0.34 CR 1b / Z+jets 0.37 0.53 7.3 0.66 0.79 CR 2 / QCD jets 0.0072 0.012 0.052 0.022 0.063 CR 3 / W+jets 0.43 0.32 1.8 0.26 0.22 CR 4 / tt¯ + single top 0.45 0.41 3.1 0.26 0.49 Table C.28.: EPS’11 Summary of CRs TFs for all SRs. From [101]. Signal / Control Region CR1a CR1b CR2 CR3 CR4 SR Data 8 7 34 15 12 18 Targeted background Z/γ+jets Z/γ+jets QCD multi-jet W+jets tt¯ + single top – Transfer factor 0.374 0.812 0.063 0.196 0.372 – Fitted Z/γ+jets 8.3 5.8 0.7 0.5 0.0 3.3 Fitted QCD multi-jet – – 29.8 0.8 0.6 2.1 Fitted W+jets – – 0.5 10.0 0.4 2.1 Fitted tt¯ + single top – 0.0 3.0 3.7 11.0 5.7 Fitted total background 8.3 5.9 34.0 15.0 12.0 13.1 Statistical uncertainty ±2.7 ±1.2 ±5.8 ±3.9 ±3.5 ±1.9 Systematic uncertainty ±0.6 ±1.7 ±0.1 ±0.1 ±0.2 ±2.5 Table C.29.: EPS’11 Numerical inputs to and outputs from the likelihood fit to the CRs for SR-E. An entry ‘–’ in rows 5–7 indicates that the process in that row is assumed not to contribute to the CR and hence excluded from the fit. All numerical entries give event counts, with the exception of the TFs row. From [102]. 240 Results from Previous Analyses As mentioned, one highlight in EPS’11 was the incorporation of both CR1a and CR1b into the likelihood fit to obtain a combined and better constrained Z + jets background estimate. With this, it was possible to incorporate SR-C that had been left out for PLHC’11. Similarly, SR-E could be incorporated, and so, this time it was possible to include all the SRs to obtain the best SUSY limits. Table C.30 shows the final results after the fitting procedure, with the Z + jets mean expectation constrained by the simultaneous measurements from CR1a and CR1b. The fitting was also performed using CR1a and CR1b individually and the results can be found in [101]. Overall, both approaches gave consistent estimates of the Z + jets background, although in SR-C the agreement was only at the limit of the fairly large uncertainties from CR1b. In conclusion, the SM expectation results from the fit were once again compatible with data and so, in absence of a significant excess, limits were again set on the same SUSY models as in PLHC’11, shown in Figure C.30. However, this time all the SRs were used, taking the best expected limit at each point, obtained by comparing the observed number of SR events (s) with those from SM background plus SUSY signal (s+ b) and using the CLs prescription [24]. In the simplified model (Figure C.30(a)), gluino/squark masses below 700 GeV/875 GeV were excluded at the 95% C.L. for squark/gluino masses below 2 TeV, with the limit increasing to 1075 GeV for equal mass squarks and gluinos. In the mSUGRA/CMSSM models (Figure C.30(b)), equal mass squarks and gluinos were excluded below 950 GeV. The EPS’11 analysis again significantly improved the reach with respect to PLHC’11. Another EPS’11 highlight was the further interpretations performed, e.g. in Universal Extra Dimensions (UED) models, which are not shown here but can be found in [118]. Process Signal Region A B C D E Z/γ+jets 32.3± 2.57± 6.87 25.5± 2.62± 4.92 209± 8.56± 38.4 16.2± 2.18± 3.67 3.25± 0.99± 1.33 W+jets 26.4± 3.97± 6.69 22.6± 3.45± 5.56 349± 30.3± 122 13± 2.18± 4.65 2.08± 0.837± 1.07 tt¯+ Single Top 3.5± 1.56± 1.59 5.9± 2.01± 2.24 425± 39.4± 84 3.99± 1.27± 2.02 5.67± 1.75± 1.94 QCD jets 0.22± 0.059± 0.24 0.92± 0.12± 0.46 34± 1.5± 29 0.73± 0.14± 0.5 2.1± 0.37± 0.82 Total 62.4± 4.37± 9.28 54.9± 3.85± 7.08 1.02e+ 03± 40.9± 144 33.9± 2.9± 6.23 13.1± 1.91± 2.49 Data 58 59 1118 40 18 Table C.30.: EPS’11 Fitted background components in each SR, compared with observation. The Z + jets background is constrained by CR1a and CR1b, while the QCD, W + jets and top backgrounds by CR2, CR3 and CR4, respectively. The values are quoted in the order ”expectation +- stat uncert +- syst uncert”. The Z + jets and W + jets are for most SRs the dominant backgrounds. From [102]. Results from Previous Analyses 241 gluino mass [GeV] 0 250 500 750 1000 1250 1500 1750 2000 sq ua rk m as s [G eV ] 0 250 500 750 1000 1250 1500 1750 2000 q~LEP2 Te va tro n, Ru n I CD F, Ru n II D 0, R un II = 10 pbSUSYσ = 1 pbSUSYσ = 0.1 pbSUSYσ = 0.01 pbSUSYσ ) = 0 GeV 1 0χ∼Squark-gluino-neutralino model, m( =7 TeVs, -1 L dt = 1.04 fb∫ 0 lepton 2011 combined ATLAS observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit 2010 data PCL 95% C.L. limit (a) [GeV]0m 500 1000 1500 2000 2500 3000 3500 [G eV ] 1/ 2 m 200 300 400 500 600 (600)g~ (800)g~ (1000)g~ (1200)g~ (600) q~ (1000) q ~ (1400) q ~ >0µ= 0, 0 = 10, AβMSUGRA/CMSSM: tan =7 TeVs, -1 L dt = 1.04 fb∫ 0 lepton 2011 combinedATLAS 1 ± χ∼LEP2 -1<0, 2.1 fbµ=3, β, tan q~, g~D0 -1<0, 2 fbµ=5, β, tan q~,g~CDF Theoretically excluded observed 95% C.L. limitsCL median expected limitsCL σ1 ±Expected limit Reference point 2010 data PCL 95% C.L. limit (b) Figure C.30.: EPS’11 combined exclusion limits for simplified SUSY models with m(χ˜01) = 0 (left) and MSUGRA/CMSSM models with tanβ = 10, A0 = 0 and µ > 0 (right). The SR with the best expected limit at each point in the parameter plane is used. The dashed-blue line corresponds to the median expected 95% C.L. limit and the red line corresponds to the observed limit at 95% C.L. The dotted blue lines correspond to the ±1σ variation in the expected limits. Also shown for comparison purposes in the figures are limits from the Tevatron and LEP (although some of these limits were produced under different models assumptions). The previous published ATLAS limits from this analysis (PLHC’11) are also shown. The mSUGRA reference point used in Figure C.29 is indicated by the star in the right-hand figure. From [101]. 242 Appendix D. Supplementary cross-checks on the method D.1. TF stand-alone estimate of Zµµ + jets (Moriond’11) At the time of the Moriond’11 analysis, the ZfromGamma method was still in early developments as it was the first time being implemented in ATLAS. As discussed in Appendix C.1, a few discrepancies were found between data and MC, which motivated the search for a cross-check of the validity of the method, that was independent of the 0` analysis to eliminate potential biases coming from it. Referred here to as the ‘Zµµ cross-check’, a summary of it is now provided. Note, however, that this cross-check has not been repeated since Moriond’11, given the good agreement of the ZfromGamma results with the Zνν + jets MC prediction in all the subsequent analysis rounds. The idea was to estimate the number of Zµµ + jets events passing a simpler (and milder) selection than the 0` SRs. This number was then to be compared to ATLAS Z + jets published results in [119]. For the event selection, the same inclusive photon sample γ + X described in Appendix C.1.3 was defined. Then, the Moriond’11 0` object definitions were applied in order to make a very simple inclusive jet channel selection: events were required to have at least one jet with pT > 30 GeV in order to match the selection in [119]. The resulting pT(γ1) distribution was then converted to a pT(Zµµ) distribution using the TF in Equation (5.6) but replacing the branching fraction Br(Z → νν) by Br(Z → µµ). Table D.1 shows the results for this estimate for prompt photon candidates with pT(γ1) > 100 GeV, where the estimate can be considered reliable 243 244 Supplementary cross-checks on the method (given the high purity of the γ +X sample in this regime). These results were compared to official ATLAS Zµµ + jets results from [119] and found to be consistent within errors. The γ + jets ALPGEN sample used in Moriond’11 to obtain the stand-alone estimate of the Zνν + jets background could not be used for this cross-check due to the 2-jet filter it had at generator-level (see Appendix C.1.2). The corresponding pT(Zµµ) distribution representing the results from Table D.1 is shown in Figure D.1. 100 GeV < pT(Zµµ) < 200 GeV Zµµ + jets Estimate Zµµ + jets Data data Pythia 286± 10(stat)± 40(syst) 289± 40(syst) 263± 25(stat)± 30(syst) Table D.1.: Moriond’11 Zµµ + jets estimate from γ+ jets data and MC from PYTHIA compared to Zµµ + jets data from [119]. [GeV] T pµµZ 100 110 120 130 140 150 160 170 180 190 200 Ev en t Y ie ld / 10 .0 G eV 1 10 210 310 -1L dt ~ 35 pb∫ Data Est.γ MC Pythia Est.γ DataµµZ ATLAS Work in Progress Figure D.1.: Moriond’11 Estimated pT(Zµµ) distribution from the γ+ ≥ 1 jet sample after correcting for acceptance, efficiency, purity and theoretical differences between the Zµµ and γ bosons, compared to actual Zµµ data from [119]. Supplementary cross-checks on the method 245 D.2. γ + jets background in 0` SRs In all the 0` analyses to date the contribution from γ+jets events to the total background estimate has been neglected so far. This has been widely accepted given that such events are not expected to pass the high EmissT requirements characterising the SRs selections – the true EmissT in γ + jets events is not expected to be large enough, as suggested by the typical values registered in even the highest pT(γ1) events e.g. see Table A.1. For this, CR1a proved useful once more to confirm such assumption. The cross-check consisted in defining the CR1a sample as usual (see Section 5.4) except for the photon “neutrification” step (see Section 3.4). Such selection was applied to the SHERPA γ + jets samples listed in Section C.3.2 and indeed it was found that no events made it into the SRs, confirming that EfakeT ′ ∼ 0 in Equation (5.2) and so, a background contribution from γ + jets events in the 0` SRs could be safely neglected. However, there was one case for which this did not apply and an actual estimate for this background had to be calculated. This was for when the effects of the ‘LAr hole’ in the data could not be neglected, corresponding to the EPS’11 analysis round (see Appendix C.3). A summary of the method to calculate it and the results now follows. D.2.1. The ‘LAr hole’ Example (EPS’11) Due to the localised hardware problems in the LAr calorimeter described in Appendix C.3 and referred to in this note as the ‘LAr hole’, an estimate was made of the additional background arising from γ+jets events that passed the EPS’11 0` SRs selections in the cases when the photon ‘fell in the hole’ and hence escaped detection and contributed to the event EmissT . This background is estimated using the γ + jets SHERPA samples listed in Table C.21. The event selection is as follows: using truth information, if the truth prompt photon is outside the LAr hole region (0 < η < 1.4 and −0.8 < φ < −0.6) the same event selection as for the SRs is applied without applying the additional “CR1a object definition” (see Section 5.4.1). However, for the cases when the truth photon does point into the LAr hole, the “CR1a object definition” is applied, which mimics the procedure used to estimate the Zνν + jets background using CR1a. Table D.2 shows the estimate central values and associated uncertainties for the γ + jets background due to the LAr hole. The systematic uncertainties are obtained by estimating the same background in a slightly 246 Supplementary cross-checks on the method larger LAr hole region (±0.1), identical to that which is used to define the LAr hole jet veto in the main SR selection (see[101]). The MC statistical uncertainty is computed from the unnormalised number of events in the SRs. The results show that this background is ∼< 8% in the SRs considered, and decreases in the higher jet multiplicity channels. Moreover, the results are a ‘conservative’ estimate since by using the true prompt photon pT, an inefficiency of 100% in the hole is assumed. This background, although small, was nevertheless included in the final 0` likelihood fit. SR Events γ+jets background Estimate Uncertainties (unnormalised) (sys) (stat) (tot) A 5 3.8 39% 45% 59% B 2 1.6 0% 71% 71% C 13 7.2 29% 28% 40% D 1 1.6 0% 100% 100% E 0 0 0% 100% 100% Table D.2.: EPS’11 Estimate of the γ+jets background due to the LAr hole and associated uncertainties using γ + jets SHERPA MC. Appendix E. List of Acronyms ALICE A Large Ion Collider Experiment AMSB Anomaly Mediated Supersymmetry Breaking ATLAS A Toroidal LHC Apparatus BCID Bunch Crossing Identification B-L Baryon-Lepton BSM Beyond-Standard-Model B.R. / Br Branching Ratio CDF Collider Detector at Fermilab CERN European Organisation for Nuclear Research CMS Compact Muon Solenoid CMSSM Constrain Minimal Supersymmetric Standard Model CP Charge-Parity CR(s) Control Region(s) CR1a Control Region 1a (the 0` CR based on γ + jets) CR1b Control Region 1b (the 0` CR based on Z`` + jets) CR2 Control Region 2 (the 0` CR based on QCD) CR3 Control Region 3 (the 0` CR based on W`ν + jets) 247 248 List of Acronyms CR4 Control Region 4 (the 0` CR based on tt¯ and single top quark) CS ATLAS Central Solenoid CSC ATLAS Cathode Strip Chambers EC ATLAS End Cap ECAL ATLAS Electromagnetic Calorimeter EM Electromagnetic EMJES ATLAS numerical inversion jet calibration scheme EPS’11 The analysis presented at the EPS conference in 2011 EW Electroweak FCNC Flavour Changing Neutral Currents FSR Final State Radiation FWD ATLAS Forward GMSB Gauge-mediated Supersymmetry Breaking GRL Good Runs List GUT Grand Unified Theories HCAL ATLAS Hadronic Calorimeter ID ATLAS Inner Detector / Identification IP Interaction Point ISR Initial State Radiation JER Jet Energy Resolution JES Jet Energy Scale LAr Liquid Argon / ATLAS Liquid Argon Calorimeter LHC Large Hadron Collider LHCb Large Hadron Collider beauty Experiment LO Leading Order List of Acronyms 249 LSP Lightest Supersymmetric Particle MC Monte Carlo MDT ATLAS Monitored Drift Tubes MET Missing Transverse Energy Moriond’11 The analysis presented at the Moriond conference in 2011 Moriond’12 The analysis presented at the Moriond conference in 2012 MS ATLAS Muon Spectrometer MSSM Minimal Supersymmetric Standard Model mSUGRA Miniman Supergravity NLO Next to Leading Order NNLO Next to Next to Leading Order NLSP Next to Lightest Supersymmetry Particle OQ Object Quality PDF(s) Parton Distribution Function(s) pdf Poisson Probability Density Function PLHC’11 The analysis presented at the PLHC conference in 2011 pQCD Perturbative QCD PR Pileup Reweighing PS Proton Synchroton PSB Proton Synchroton Booster PU Pileup PV Primary Vertex QED Quantum Electrodynamics QCD Quantum Chromodynamics RF Radio Frequency 250 List of Acronyms RGE Renormalisation Group Equations RPC R-parity Conservation / ATLAS Resistive Plate Chambers RPV R-parity Violation SCT ATLAS Silicon Tracker SM Standard Model SMDP Standard Model Direct Photon SPS Super Proton Synchroton SR(s) Signal Region(s) SUGRA Supergravity SUSY Supersymmetry TF(s) Transfer Function(s) / Transfer Factor(s) TGC ATLAS Thin Gap Chambers TRT ATLAS Transition Radiation Tracker UE Underlying Event WIMP Weakly Interacting Massive Particle 0` Zero Lepton (analysis) 252 Bibliography [1] F. 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Abreu et al., CERN Report No. ATL-PHYS-INT-2011-037, 2011 (unpublished). [117] ATLAS SM Direct Photon Working Group Recommendations, https://twiki. cern.ch/twiki/bin/viewauth/AtlasProtected/PhotonCrossSection2011. [118] T.-J. Khoo, M. Rammensee, Z. Rurikova, N. Kanaya, and P. De Jong, CERN Report No. ATLAS-COM-CONF-2011-183, 2011 (unpublished). [119] H. Bauchemin et al., CERN Report No. ATL-COM-PHYS-2011-141, 2011 (unpub- lished). 260 List of Figures 1.1. Example of loop corrections to photon propagator . . . . . . . . . . . . . 11 1.2. The parton model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3. Proton structure functions and PDFs . . . . . . . . . . . . . . . . . . . . 13 1.4. The running of αS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5. Parton showering and hadronisation . . . . . . . . . . . . . . . . . . . . . 15 1.6. Underlying Event in hadron-hadron collisions . . . . . . . . . . . . . . . 15 1.7. Electroweak and QCD tests of the SM . . . . . . . . . . . . . . . . . . . 17 1.8. SM problems fixed by SUSY . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.9. An mSUGRA mass spectrum . . . . . . . . . . . . . . . . . . . . . . . . 25 1.10. LHC’s sensitivity to SUSY . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.11. SUSY phenomenology at the LHC . . . . . . . . . . . . . . . . . . . . . . 27 1.12. ATLAS strategy for New Physics searches . . . . . . . . . . . . . . . . . 29 2.1. LHC layout and operation cycle . . . . . . . . . . . . . . . . . . . . . . . 36 2.2. LHC cumulative and peak luminosities delivered in 2011 . . . . . . . . . 37 2.3. LHC performance in 2011 . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4. ATLAS coordinate system and plan view . . . . . . . . . . . . . . . . . . 42 2.5. ATLAS detector computer generated image . . . . . . . . . . . . . . . . 43 2.6. ATLAS Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . 46 261 262 LIST OF FIGURES 2.7. ATLAS Trigger/DAQ system . . . . . . . . . . . . . . . . . . . . . . . . 48 2.8. Trigger prescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.9. ATLAS cumulative luminosity recorded in 2011 . . . . . . . . . . . . . . 50 2.10. ATLAS performance in 2011 . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.11. ATLAS pileup environment in 2011 . . . . . . . . . . . . . . . . . . . . . 52 2.12. ATLAS event display of a prompt photon and pi0 candidate . . . . . . . . 55 3.1. Zνν , W`ν and γ pT and the Z/γ ratio . . . . . . . . . . . . . . . . . . . . 66 3.2. The ZfromGamma method . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.1. Feynman diagrams for Z/γ + 1, 2 jets . . . . . . . . . . . . . . . . . . . . 74 4.2. d/u quark PDFs and the RZ/γ dependence on them . . . . . . . . . . . . 75 4.3. GAMBOS Z and γ pT at √ s = 7 TeV and 14 TeV and their ratio RZ/γ . . . 77 4.4. PYTHIA Z and γ pT at √ s = 7 TeV and 14 TeV and their ratio RZ/γ . . . 79 4.5. Effect on Z/γ pT from GAMBOS and PYTHIA at √ s = 7 TeV and 14 TeV . . 79 4.6. Effect on d(x)/u(x) from different PDFs . . . . . . . . . . . . . . . . . . 80 4.7. PYTHIA- Effect on Z/γ pT and RZ/γ from different PDFs . . . . . . . . . 81 4.8. PYTHIA- Effect on Z/γ pT and RZ/γ from different µ scales . . . . . . . . 82 4.9. Expected effect on αS from using different scales in RZ/γ . . . . . . . . . 83 4.10. GAMBOS- Effect on RZ/γ from different isolation cuts ∆R . . . . . . . . . . 84 4.11. GAMBOS and PYTHIA- Effect on RZ/γ from different jet multiplicities . . . 85 4.12. PYTHIA- γ isolation ET(pT) and RZ/γ at parton and reconstruction level . 87 4.13. PYTHIA- Z/γ pT and η after a 2-jet SUSY selection . . . . . . . . . . . . 88 4.14. PYTHIA- Z/γ pT and η after a 3-jet SUSY selection . . . . . . . . . . . . 89 4.15. PYTHIA- Zνν pT after 2/3-jet SUSY selections compared to γ estimate . . 91 LIST OF FIGURES 263 5.1. Moriond’11 and Moriond’12 γ EisoT distribution after the γ +X selection 108 5.2. Moriond’12 prompt photon pT and η after the γ +X selection . . . . . . 110 5.3. Moriond’11 photon pT under different γ +X selection stages . . . . . . . 113 5.4. CR1a object definitions and event selection . . . . . . . . . . . . . . . . . 119 5.5. CR1a γ-jet separation criterion for overlap removal . . . . . . . . . . . . 120 5.6. PLHC’11 Effect of different EmissT algorithms in γ + jets and Zνν + jets . 120 5.7. Moriond’12 Effect of different EmissT algorithms on the γ +X sample . . . 121 5.8. PLHC’11 Effect of the 0` selection on the photon Fside shower shape . . 126 5.9. Moriond’12 CR1a prompt photon pT . . . . . . . . . . . . . . . . . . . . 128 5.10. Moriond’12 CR1a meff(incl.) distribution . . . . . . . . . . . . . . . . . . 129 5.11. Moriond’12 Event display of the highest prompt photon pT event . . . . 130 5.12. Illustration of the effect of the TF on the CR . . . . . . . . . . . . . . . . 132 5.13. Moriond’12 Aγ(pT) · εγ(pT) at different 0` selection stages . . . . . . . . . 134 5.14. Moriond’12 CR1a RZ/γ(pT) for each SR . . . . . . . . . . . . . . . . . . . 139 5.15. Moriond’11 photon η at different 0` selection stages . . . . . . . . . . . . 140 5.16. Moriond’12 Zνν + jets meff(incl.) from γ + jets estimate and Zνν + jets MC142 5.17. Moriond’12 meff(incl.) for CR1a, CR1b and CR3 for SR-A . . . . . . . . 149 5.18. Moriond’12 meff(incl.) for each 0` SR . . . . . . . . . . . . . . . . . . . . 155 5.19. Moriond’12 0` limits on SUSY models . . . . . . . . . . . . . . . . . . . 163 5.20. Moriond’12 Effect of CR1a Zνν + jets estimate on 0` limits . . . . . . . . 164 6.1. Moriond’12 CMS MHT+jets search - event counts and background predic- tion in SRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 6.2. Moriond’12 CMS MHT+jets search - γ + jets control sample . . . . . . . 169 6.3. Moriond’12 CMS MT2 search - γ + jets control sample . . . . . . . . . . 170 6.4. Moriond’12 CMS MT2 search - Zνν + jets estimate and RZ/γ . . . . . . . 171 264 LIST OF FIGURES 6.5. ATLAS SUSY searches 2011 summary plot . . . . . . . . . . . . . . . . . 172 6.6. ATLAS Exotics searches 2011 summary plot . . . . . . . . . . . . . . . . 174 A.1. Moriond’12 event display of the 2nd highest prompt photon pT event . . 178 A.2. Moriond’12 event display of the 3rd & 4th highest prompt photon pT events179 B.1. SMDP photon trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . 183 B.2. SMDP reconstruction efficiency εγrec . . . . . . . . . . . . . . . . . . . . . 184 B.3. SMDP identification efficiency εγid . . . . . . . . . . . . . . . . . . . . . . 185 B.4. SMDP signal yield and purity . . . . . . . . . . . . . . . . . . . . . . . . 188 B.5. SMDP isolation energy EisoT for different photon pT and η . . . . . . . . . 189 C.1. Moriond’11 prompt photon pT and η after the γ +X selection . . . . . . 195 C.2. Moriond’11 leading jet pT distribution in the γ +X sample . . . . . . . . 195 C.3. Moriond’11 photon shower shape variables . . . . . . . . . . . . . . . . . 196 C.4. Moriond’11 prompt photon pT at different 0` selection stages . . . . . . . 199 C.5. Moriond’11 leading jet pT at different 0` selection stages . . . . . . . . . 200 C.6. Moriond’11 effect of 0` selections on shower shape Eratio . . . . . . . . . . 201 C.7. Moriond’11 Zνν + jets E miss T from γ + jets compared to Zνν + jets MC . . 204 C.8. Moriond’11 SRs meff in data and MC . . . . . . . . . . . . . . . . . . . . 205 C.9. Moriond’11 0` limits on SUSY models . . . . . . . . . . . . . . . . . . . 206 C.10.PLHC’11 prompt photon pT after the γ +X selection . . . . . . . . . . . 210 C.11.PLHC’11 prompt photon pT evolution with the 0` selection . . . . . . . . 212 C.12.PLHC’11 effect of missing multijets in γ + jets PYTHIA . . . . . . . . . . 212 C.13.PLHC’11 effect of MC pileup reweighing in the prompt photon pT . . . . 213 C.14.PLHC’11 CR1a meff for each SR . . . . . . . . . . . . . . . . . . . . . . . 214 LIST OF FIGURES 265 C.15.PLHC’11 Aγ(pT) · εγ(pT) in SR-A with softer meff cut . . . . . . . . . . . 217 C.16.PLHC’11 Zνν + jets meff estimated from γ + jets compared to Zνν + jets MC218 C.17.PLHC’11 0` SRs meff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 C.18.PLHC’11 0` limits on SUSY models . . . . . . . . . . . . . . . . . . . . . 223 C.19.EPS’11 mean number of interactions per bunch crossing 〈µ〉 . . . . . . . 226 C.20.EPS’11 prompt photon pT after the γ +X selection . . . . . . . . . . . . 228 C.21.EPS’11 event display of the highest pT prompt photon event . . . . . . . 229 C.22.EPS’11 prompt photon pT evolution with the 0` selections . . . . . . . . 230 C.23.EPS’11 CR1a meff SHERPA-70 with pileup reweighing . . . . . . . . . . . 231 C.24.EPS’11 CR1a meff SHERPA-70 with no pileup reweighing . . . . . . . . . 232 C.25.EPS’11 CR1a meff vs pT(γ1) in SHERPA-70 and SHERPA-140 without PR . 233 C.26.EPS’11 true and reconstructed pT(γ1) in SHERPA-70 and SHERPA-140 . . . 233 C.27.EPS’11 final CR1a meff used in 0` analysis . . . . . . . . . . . . . . . . . 234 C.28.EPS’11 Zνν + jets meff estimated from γ + jets compared to Zνν + jets MC237 C.29.EPS’11 0` SRs meff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 C.30.EPS’11 0` limits on SUSY models . . . . . . . . . . . . . . . . . . . . . . 241 D.1. Moriond’11 estimated pT(Zµµ) from γ + jets compared to Zµµ data . . . 244 266 List of Tables 1.1. SM couplings and gauge fields . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. SM free parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3. MSSM field content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4. Mixing in the MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5. SUSY canonical scenario phenomenology . . . . . . . . . . . . . . . . . . 27 1.6. ATLAS SUSY RPC searches - Targets . . . . . . . . . . . . . . . . . . . 30 1.7. ATLAS SUSY RPC searches - Signal Regions . . . . . . . . . . . . . . . 30 1.8. ATLAS SUSY RPC searches - Backgrounds . . . . . . . . . . . . . . . . 31 2.1. LHC-Tevatron comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2. LHC timeline from Sept 2008 to Oct 2011 . . . . . . . . . . . . . . . . . 39 2.3. LHC variation of peak luminosity with beam parameters . . . . . . . . . 39 2.4. ATLAS subsystems acceptance and resolution . . . . . . . . . . . . . . . 43 2.5. Examples of the photon triggers used and their estimated efficiencies. Uncertainties are statistical only. In the trigger name, “g” is for “gamma”, the number represents the ET threshold and “loose” the type of ID requirement. From[43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1. GAMBOS and PYTHIA- Values of RZνν/γ after SUSY selections and uncertainties 92 5.1. ATLAS ZfromGamma software framework . . . . . . . . . . . . . . . . . . 97 5.2. ATLAS data samples used for the different analyses . . . . . . . . . . . . 99 267 268 LIST OF TABLES 5.3. Moriond’12 γ + jets MC samples . . . . . . . . . . . . . . . . . . . . . . 102 5.4. Moriond’12 Zνν + jets MC samples . . . . . . . . . . . . . . . . . . . . . 102 5.5. Moriond’12 top background to γ + jets MC samples . . . . . . . . . . . . 103 5.6. Moriond’12 vector boson background to γ + jets MC samples . . . . . . . 104 5.7. ATLAS MC production details for the different analyses . . . . . . . . . 105 5.8. Photon object definitions in the different analyses . . . . . . . . . . . . . 108 5.9. Event selection for the γ +X sample in the different anlayses . . . . . . 109 5.10. Cutflow for the γ +X event selection in the different analyses . . . . . . 110 5.11. Control Regions defined in the 0` analysis . . . . . . . . . . . . . . . . . 116 5.12. CR1a EfakeT and E true T definitions in the different analyses . . . . . . . . . 118 5.13. Moriond’12 summarised event selection for the 0` SRs . . . . . . . . . . . 123 5.14. Moriond’12 detailed event selection for the 0` SRs . . . . . . . . . . . . . 124 5.15. Moriond’12 CR1a data event counts for all 0` SRs . . . . . . . . . . . . . 127 5.16. CR1a range and average prompt photon pT in the different analyses . . . 127 5.17. η acceptance of true photons in the different analyses . . . . . . . . . . . 133 5.18. Moriond’12 efficiency of isolation energy εγiso . . . . . . . . . . . . . . . . 135 5.19. Moriond’12 CR1a event counts in the SRs . . . . . . . . . . . . . . . . . 143 5.20. Moriond’12 CR1a TF central values and uncertainties . . . . . . . . . . . 145 5.21. Moriond’12 0` CRs event selections . . . . . . . . . . . . . . . . . . . . . 148 5.22. Moriond’12 data event counts in the SR and CRs . . . . . . . . . . . . . 150 5.23. Moriond’12 summary of TFs central values for each SR . . . . . . . . . . 150 5.24. Moriond’12 cross-TFs for SR-A medium . . . . . . . . . . . . . . . . . . 150 5.25. Moriond’12 event counts and fitted background for each SR . . . . . . . . 153 5.26. Moriond’12 contributions from the different backgrounds to the SR . . . 154 5.27. Moriond’12 range, mean and standard deviation of all TFs . . . . . . . . 157 LIST OF TABLES 269 5.28. Moriond’12 uncertainties on the TFs to SR-A medium . . . . . . . . . . 159 5.29. Moriond’12 influence of uncertainties in the SRs . . . . . . . . . . . . . . 160 5.30. Moriond’12 limits on σSUSY · A · ε . . . . . . . . . . . . . . . . . . . . . . 162 A.1. Moriond’12 event display details of the highest pT prompt photon events 177 B.1. SMDP reconstruction efficiency εγrec . . . . . . . . . . . . . . . . . . . . . 184 B.2. SMDP identification efficiency εγid . . . . . . . . . . . . . . . . . . . . . . 185 B.3. SMDP signal yield and purity . . . . . . . . . . . . . . . . . . . . . . . . 187 C.1. Moriond’11 ATLAS data streams used . . . . . . . . . . . . . . . . . . . 192 C.2. Moriond’11 γ + jets MC samples . . . . . . . . . . . . . . . . . . . . . . 193 C.3. Moriond’11 QCD background to γ + jets MC samples . . . . . . . . . . . 193 C.4. Moriond’11 Zνν + jets MC samples . . . . . . . . . . . . . . . . . . . . . 193 C.5. Moriond’11 γ +X event selection . . . . . . . . . . . . . . . . . . . . . . 194 C.6. Moriond’11 0` SRs event selection . . . . . . . . . . . . . . . . . . . . . . 197 C.7. Moriond’11 Zνν + jets estimate from γ + jets compared to Zνν + jets MC 203 C.8. Moriond’11 0` final event numbers results in each SR . . . . . . . . . . . 206 C.9. PLHC’11 γ + jets MC samples . . . . . . . . . . . . . . . . . . . . . . . . 208 C.10.PLHC’11 Zνν + jets MC samples . . . . . . . . . . . . . . . . . . . . . . 209 C.11.PLHC’11 0` SRs event selections . . . . . . . . . . . . . . . . . . . . . . 211 C.12.PLHC’11 CR1a percentage loss in MC statistics from pileup reweighing . 211 C.13.PLHC’11 CR1a TFs central values and uncertainties . . . . . . . . . . . 215 C.14.PLHC’11 effect from pileup reweighing on CR1a Aγ(pT) · εγ(pT) . . . . . 217 C.15.PLHC’11 Zνν + jets estimate from γ + jets compared to Zνν + jets MC . 218 C.16.PLHC’11 data event counts in all the 0` SRs and CRs . . . . . . . . . . 221 270 LIST OF TABLES C.17.PLHC’11 CRs TFs summary . . . . . . . . . . . . . . . . . . . . . . . . . 221 C.18.PLHC’11 CRs TF and uncert’s for SR-C . . . . . . . . . . . . . . . . . . 222 C.19.PLHC’11 0` fitted background in SRs using CR1a . . . . . . . . . . . . . 222 C.20.[PLHC’11 0` fitted background in SRs using CR1b . . . . . . . . . . . . 223 C.21.EPS’11 γ + jets MC samples . . . . . . . . . . . . . . . . . . . . . . . . . 226 C.22.EPS’11 Zνν + jets MC samples . . . . . . . . . . . . . . . . . . . . . . . . 226 C.23.EPS’11 scaling factors applied to SHERPA-140 CR1a meff . . . . . . . . . 230 C.24.EPS’11 CR1a TFs central values and uncertainties . . . . . . . . . . . . 235 C.25.EPS’11 Zνν + jets estimate from γ + jets compared to Zνν + jets MC . . 236 C.26.EPS’11 data event counts in all SRs and CRs . . . . . . . . . . . . . . . 237 C.27.EPS’11 0` background expectation from MC . . . . . . . . . . . . . . . . 239 C.28.EPS’11 summary of CRs TFs . . . . . . . . . . . . . . . . . . . . . . . . 239 C.29.EPS’11 0` likelihood fit to the CRs for SR-E . . . . . . . . . . . . . . . . 239 C.30.EPS’11 0` fitted background in each SR . . . . . . . . . . . . . . . . . . 240 D.1. Moriond’11 Zµµ + jets estimate from γ + jets compared to Zµµ + jets data 244 D.2. EPS’11 estimate of γ + jets background in the 0` SRs due to LAr hole . 246