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Parton Distributions with Theory Uncertainties: General Formalism and First Phenomenological Studies

Published version
Peer-reviewed

Type

Article

Change log

Authors

Collaboration, The NNPDF 
Khalek, Rabah Abdul 
Ball, Richard D 
Carrazza, Stefano 
Forte, Stefano 

Abstract

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology. In addition, we also compare the results based on the theory covariance matrix formalism to those obtained by performing PDF determinations based on different scale choices.

Description

Keywords

hep-ph, hep-ph, hep-ex

Journal Title

European Physical Journal C: Particles and Fields

Conference Name

Journal ISSN

1124-1861
1434-6052

Volume Title

79

Publisher

Springer Nature

Rights

All rights reserved
Sponsorship
Science and Technology Facilities Council (ST/J000434/1)
Royal Society (DH150088)
Royal Society (RGF/EA/180148)
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/R504671/1)
Science and Technology Facilities Council (ST/P000681/1)
STFC (1948592)
European Research Council (683211)