Higgs boson properties are studied in the four-lepton decay channel (where lepton =
O. Igonkina, B.T. King, D. Lellouch: Deceased.
The original online version of this article was revised: In the published HTML version of this article, some affiliations of the author had been interchanged. The original article has been corrected.
An erratum to this article is available online at
An erratum to this article is available online at
corrected publication 2020
The observation of the Higgs boson by the ATLAS and CMS experiments [
Motivated by a clear Higgs boson signature and a high signal-to-background ratio in the
In addition to a nearly four times higher integrated luminosity, there are several other important differences compared to the previous results in this analysis channel [ an improved lepton isolation to mitigate the impact of additional an improved jet reconstruction using a particle flow algorithm [ additional event categories for the classification of Higgs boson candidates, new discriminants to enhance the sensitivity to distinguish the various production modes of the SM Higgs boson, the use of data sidebands to constrain the dominant a dedicated control region to constrain the background in the reconstructed event categories probing improved estimates of an EFT interpretation, based on a parameterisation of the cross-sections rather than a direct parameterisation of the reconstructed event yields.
In the framework of
The definitions of the production bins used for this measurement are shown in the left panel of Fig. Two sets (Production Mode Stage and Reduced Stage 1.1) of exclusive phase-space regions (production bins) defined at particle-level for the measurement of the Higgs boson production cross-sections (left and middle-left shaded panels), and the corresponding reconstructed event categories for signal (middle-right panel) and sidebands (right panel). The description of the production bins is given in Sect.
The first set of production bins (Production Mode Stage) [
The second set of production bins (Reduced Stage 1.1) is more exclusive than the first one. Starting from the production bins of a more granular Stage 1.1 set [
Events from
As described in Ref. [
The
The middle-right and right panels of Fig.
To probe physics beyond the SM, the measured production cross-sections are interpreted within a leading-order-motivated
The
Constraints are set on the Wilson coefficients defined within the Standard Model Effective Field Theory (SMEFT) formalism [ Summary of EFT operators in the SMEFT formalism that are probed in the CP-even CP-odd Impact on Operator Structure Coeff. Operator Structure Coeff. production decay - Yes Yes Yes Yes
The remaining ten operators (see Table
The constraints on the Wilson coefficients can be derived by comparing the expected with the measured simplified template cross-sections. For that purpose, the corresponding expected signal production cross-sections, the branching ratio and the signal acceptances are parameterised in terms of the Wilson coefficients. The dependence of signal production cross-sections on the EFT parameters can be obtained from its separation into three components:
The ATLAS detector [
The full ATLAS Run 2 data set, consisting of
The production of the SM Higgs boson via gluon–gluon fusion, via vector-boson fusion, with an associated vector boson and with a top quark pair was modelled with the
The simulation of
The matrix elements of the
The production of a Higgs boson in association with a bottom quark pair (
For all production mechanisms, the
For additional cross-checks, the
The Higgs boson production cross-sections and decay branching ratios, as well as their uncertainties, are taken from Refs. [ The predicted SM Higgs boson production cross-sections ( Production process Decay process
For the study of the tensor structure of Higgs boson couplings within an effective field theory approach, several samples with different values of EFT parameters were simulated at LO in QCD separately for the
The
The gluon-induced
Production of
For all
For additional checks, the
The
The simulation of
The modelling of events containing
The
Generated events were processed through the ATLAS detector simulation [
The selection and categorisation of the Higgs boson candidate events rely on the reconstruction and identification of electrons, muons, and jets, closely following the analyses reported in Refs. [
Proton–proton collision vertices are constructed from reconstructed trajectories of charged particles in the ID with transverse momentum
Electron candidates are reconstructed from energy clusters in the electromagnetic calorimeter that are matched to ID tracks [
Muon candidate reconstruction [
Jets are reconstructed using a particle flow algorithm [
Ambiguities are resolved if electron, muon, or jet candidates overlap in geometry or share the same detector information. If the two calorimeter energy clusters from the two electron candidates overlap, the electron with the higher
The missing transverse momentum vector,
A summary of the event selection criteria is given in Table Summary of the criteria applied to the selected Higgs boson candidate in each event. The mass threshold Combination of single-lepton, dilepton and trilepton triggers All combinations of two same-flavour and opposite-charge lepton pairs – Leading lepton pair: lepton pair with invariant mass – Subleading lepton pair: lepton pair with invariant mass Classification according to the decay final state: 4 – Three highest- – At most one calorimeter-tagged or stand-alone muon – Leading lepton pair: – Subleading lepton pair: – Alternative same-flavour opposite-charge lepton pair: – – The amount of isolation calorimeter-based contribution must be smaller than 16% of the lepton - Electrons: – Muons: – – Select quadruplet with – If at least one additional (fifth) lepton with the quadruplet with the highest matrix-element value – Correction of the four-lepton invariant mass due to the FSR photons in – Four-lepton invariant mass window in the signal region: – Four-lepton invariant mass window in the sideband region:
In the analysis, at least two same-flavour and opposite-charge lepton pairs (hereafter referred to as lepton pairs) are required in the final state, resulting in one or more possible lepton quadruplets in each event. The three highest-
The lepton pair with the invariant mass
To ensure that the leading lepton pair from the signal originates from a
Each electron (muon) track is required to have a transverse impact parameter significance
The four quadruplet leptons are required to originate from a common vertex point. A requirement corresponding to a signal efficiency of better than 99.5% is imposed on the
If there is more than one decay final state per event with the priority quadruplet (
In the case of
To improve the four-lepton invariant mass reconstruction, the reconstructed final-state radiation (FSR) photons in
Collinear FSR candidates are selected from reconstructed photon candidates and from electron candidates that share an ID track with the muon. Further criteria are applied to each candidate, based on the following discriminants: the fraction,
Only one FSR candidate is included in the quadruplet, with preference given to collinear FSR and to the candidate with the highest
The Higgs boson candidates within a mass window of 115
The selection efficiencies of the simulated signal in the fiducial region Impact on the expected invariant mass distribution of the selected Higgs boson candidates due to (
In order to be sensitive to different production bins in the framework of simplified template cross-sections, the selected Higgs boson candidates in the mass window
For signal events, the classification is performed in the order shown in the middle-right panel of Fig.
The remaining events are classified according to their reconstructed jet multiplicity into events with no jets, exactly one jet or at least two jets. Events with at least two reconstructed jets are divided into two categories: one is a ‘BSM-like’ category (
Events with zero or one jet in the final state are expected to be mostly from the
The largest number of
As illustrated in Fig.
The rightmost panel of Fig.
For the estimation of non-resonant
The expected number of signal events is shown in Table
The separation of the contributions from different production bins, such as the The expected number of SM Higgs boson events with Reconstructed event category SM Higgs boson production mode Signal Sideband SB- SB- SB- SB- SB- Total
Standard Model signal composition in terms of the Reduced Stage-1.1 production bins in each reconstructed event category. The
To further increase the sensitivity of the cross-section measurements in the production bins (Sect.
Two types of NNs are used: feed-forward multilayer perceptron (MLP) and recurrent (RNN) [ The input variables used to train the MLP, and the two RNNs for the four leptons and the jets (up to three). For each category, the processes which are classified by an NN, their corresponding input variables and the observable used are shown. For example, there are eight input variables for the Lepton RNN being trained if Category Processes MLP Lepton RNN Jet RNN Discriminant – – – – –
The NN training variables not previously defined are listed as follows. The kinematic discriminant
Depending on the category and the number of processes being targeted, the NN has two or three output nodes. The value computed at each node represents the probability, with an integral of one, for the event to originate from the given process. For example, for the 0-jet category, two probabilities are evaluated,
Non-resonant SM
As outlined in Sect. The observed and expected (post-fit) distributions for an integrated luminosity of 139 fb
Similarly, backgrounds affecting the
The contribution from
Other processes, such as
In the
The control regions used to estimate this background are defined by closely following the requirements outlined in Sect. an enhanced heavy-flavour control region with inverted impact-parameter and relaxed isolation requirements on the subleading lepton pair and relaxed vertex an enhanced an enhanced light-flavour control region with inverted isolation requirements for at least one lepton in the subleading lepton pair, and a same-sign
The first two are the primary control regions used to estimate
The background normalisations are obtained separately for the
The
The remaining background is separated into light-flavour and photon conversion background components using the sPlot method [
The systematic uncertainties are categorised into experimental and theoretical uncertainties. The first category includes uncertainties in lepton and jet reconstruction, identification, isolation and trigger efficiencies, energy resolution and scale, and uncertainty in the total integrated luminosity. Uncertainties from the procedure used to derive the data-driven background estimates are also included in this category. The second category includes uncertainties in theoretical modelling of the signal and background processes.
The uncertainties can affect the signal acceptance, selection efficiency and discriminant distributions as well as the background estimates. The dominant sources of uncertainty and their effect are described in the following subsections. The impact of these uncertainties on the measurements is summarised in Table The impact of the dominant systematic uncertainties (in percent) on the cross-sections in production bins of the Production Mode Stage and the Reduced Stage 1.1. Similar sources of systematic uncertainties are grouped together: luminosity (Lumi.), electron/muon reconstruction and identification efficiencies and pile-up modelling ( Measurement Experimental uncertainties [%] Theory uncertainties [%] Lumi. Jets, Reducible Background Signal pile-up flav. tag bkg PDF QCD Shower Inclusive cross-section 1.7 2.5 1 2 Production mode cross-sections 1.7 2.5 1 1.5 0.5 1 2 1.7 2 4 1.5 1 5 7 1.9 2 4 1 6 2 13.5 7.5 1.7 2 6 1 0.5 0.5 12.5 4 Reduced Stage-1.1 production bin cross-sections 1.7 3 1.5 0.5 6.5 1 1.5 1.7 3 5 3 0.5 5.5 1.7 2.5 12 0.5 7 1 6 1.7 3 7.5 1 1.5 5.5 1.7 3 11 0.5 2 2 7.5 1.7 2.5 16.5 1 12.5 0.5 2.5 10.5 1.7 1.5 3 0.5 3.5 2 3.5 1.8 4 17 1 4 1 0.5 5.5 8 1.7 2 3.5 5 6 10.5 1.7 2 4 2.5 3 8 1.8 2.5 2 1 2 0.5 1.5 3 1.7 2.5 5 0.5 1 0.5 11 3
The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% [
The uncertainty in the predicted yields due to pile-up modelling ranges between 1% and 2% and is derived by varying the average number of pile-up events in the simulation to cover the uncertainty in the ratio of the predicted to measured inelastic cross-sections [
The electron (muon) reconstruction, isolation and identification efficiencies, and the energy (momentum) scale and resolution are derived from data using large samples of
The uncertainties in the jet energy scale and resolution are in the range 1%–3% [
The uncertainty in the calibration of the
A shift in the simulated Higgs boson mass corresponding to the precision of the Higgs boson measurement,
For the data-driven measurement of the reducible background, three sources of uncertainty are considered: statistical uncertainty, overall systematic uncertainty for each of
The theoretical modelling of the signal and background processes is affected by uncertainties due to missing higher-order corrections, modelling of parton showers and the underlying event, and PDF
The impact of the theory systematic uncertainties on the signal depends on the kind of measurement that is performed. For signal-strength measurements, defined as the measured cross-section divided by the SM prediction, or interpretation of cross-section using the EFT approach, each source of theory uncertainty affects both the acceptance and the predicted SM cross-section. For the cross-section measurements, only effects on the acceptance need to be considered.
The impact of the theory systematic uncertainties on the background depends on the method of estimating the normalisation. If simulation is used, the uncertainties in the acceptance and the predicted SM cross-section are included. If the normalisation is estimated from a data-driven method, only the impact on the relative event fractions between categories is considered.
One of the dominant sources of theoretical uncertainty is the prediction of the
For the
For the
The uncertainties in the acceptance due to the modelling of parton showers and the underlying event are estimated with AZNLO tune eigenvector variations and by comparing the acceptance using the parton showering algorithm from
The impact of the PDF uncertainty is estimated with the thirty eigenvector variations of the
The impacts of the theoretical uncertainties, as described above, on the shape of NN discriminants are also considered. For
For signal-strength measurements, an additional uncertainty related to the
Since the normalisation of the
The uncertainty in the gluon-initiated and the vector-boson-initiated
For the
Uncertainties in the PDF and in missing higher-order corrections in QCD are applied to the
To probe the tensor structure of the Higgs boson coupling in the EFT approach, theoretical uncertainties due to PDF and QCD scale variations are assigned to the signal predictions based on the simulated highest-order SM signal samples. The same uncertainties are assigned to all corresponding BSM signal predictions, since it is shown using the MC signal samples simulated at LO accuracy that the uncertainties change negligibly as a function of the Wilson coefficients. The observed and expected (post-fit) four-lepton invariant mass distributions for the selected Higgs boson candidates, shown for an integrated luminosity of
The expected and observed four-lepton invariant mass (post-fit) distributions of the selected Higgs boson candidates after the event selection are shown in Fig.
The observed and expected (post-fit) distributions of the jet multiplicity, the dijet invariant mass, and the four-lepton transverse momenta in different
The expected numbers of signal and background events in each reconstructed event category are shown in Table
The statistical interpretation of the results and compatibility with the SM are discussed in the following. The observed and expected distributions (post-fit) of ( The expected (pre-fit) and observed numbers of events for an integrated luminosity of 139 fb Reconstructed event category Signal Other Total Observed background background backgrounds expected Signal 56 117 1 41 31 4 2 48 6 1 2 1 Sideband SB- 183 SB- 64 SB- 41 SB- 3 SB- 19
To measure the product
Assuming that the relative signal fractions in each production bin are given by the predictions for the SM Higgs boson, the inclusive
The SM prediction is
The corresponding likelihood functions are shown in Fig.
The expected SM cross-section, the observed values of
The corresponding values are summarised in Fig. The observed and expected NN output (post-fit) distributions for an integrated luminosity of 139 fb The observed and expected NN output (post-fit) distributions for an integrated luminosity of 139 fb Observed profile likelihood as a function of ( The expected SM cross-section Production bin Cross-section ( SM expected Observed Observed Inclusive production, Production Mode Stage bins, Reduced Stage-1.1 bins,
The observed and expected SM values of the cross-sections
For the
The dominant contribution to the measurement uncertainty in the
Figure Likelihood contours at 68% CL (dashed line) and 95% CL (solid line) in the (
The cross-sections measured at the Production Mode Stage are interpreted in the
To interpret the observed data in the framework of an effective field theory, an EFT signal model is built by parameterising the production cross-sections in each production bin of the Reduced Stage 1.1, as well as the branching ratio and the signal acceptances, as a function of the SMEFT Wilson coefficients introduced in Sect.
The EFT parameterisation of the production cross-sections in each production bin of the Reduced Stage 1.1 is obtained from Eq. ( Likelihood contours at 68% CL (dashed line) and 95% CL (solid line) in the
The branching ratio for the
The selection criteria for the four-lepton Higgs boson candidates, in particular the requirements on the minimum invariant mass
The final parameterisation of signal yields relative to the SM prediction in each production bin of the Reduced Stage 1.1 is obtained as the product of the corresponding cross-section, branching ratio and acceptance parameterisations. The expected event yields normalised to the SM prediction are shown in Fig.
The ratios of the expected signal yield for a chosen EFT parameter value to its SM prediction are shown in Fig. The dependence of the signal acceptance normalised to the SM acceptance on the Wilson coefficients ( The expected event yields ( The expected signal yield ratio for chosen ( The observed and expected values of SMEFT Wilson coefficients from ( The expected and observed confidence intervals at 68% and 95% CL on the SMEFT Wilson coefficients for an integrated luminosity of 139 EFT coupling parameter Expected Observed Best-fit Best-fit 68% CL 95% CL 68% CL 95% CL value [ [ [ [ 0.79 [ [ [ [ 0.50 [ [ [ [ 0.5 0.66 [ [ [ [ 0.98 [ [ [ [ 0.1 0.93 [ [ [ [ 0.000 1.00 [ [ [ [ 0.48 [ [ [ [ 0.84 [ [ [ [ 0.00 1.00 [ [ [ [ 0.0 1.00
The EFT parameterisation of signal yields is implemented in the likelihood function of Eq. (
The fit results with only one Wilson coefficient fitted at a time are summarised in Fig. Expected (dashed line) and observed (full line) 2D-fit likelihood curves at the 95% CL for the SMEFT Wilson coefficients of CP-even operators at an integrated luminosity of Expected (dashed line) and observed (full line) 2D-fit likelihood curves at the 95% CL for the SMEFT Wilson coefficients of CP-odd operators at an integrated luminosity of
The strongest constraint, driven mostly by the
To explore possible correlations between different Wilson coefficients, the simultaneous fits are also performed on two Wilson coefficients at a time. The corresponding results are shown in Fig. The best-fit values and the corresponding deviation from the SM prediction obtained from the two-dimensional likelihood scans of the CP-odd BSM coupling parameters performed with 139 BSM coupling parameter Observed best fit Best-fit 0.88 0.78 0.80 0.91 1.00 0.78
The anti-correlation between the
The ‘V’-shaped correlation between the
The correlation between the
Higgs boson properties are studied in the four-lepton decay channel using
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russia Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; ERC, ERDF, Horizon 2020, Marie Skłodowska-Curie Actions and COST, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom.
The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (
ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the
The transverse impact parameter
The additional lepton is a lepton candidate as defined in Sect.