https://doi.org/10.1140/epjc/s10052-019-7401-4
Regular Article - Theoretical Physics
Parton distributions with theory uncertainties: general formalism and first phenomenological studies
NNPDF Collaboration
1
Department of Physics and Astronomy, VU University, 1081 HV, Amsterdam, The Netherlands
2
Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
3
The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd, Edinburgh, Scotland, EH9 3JZ, UK
4
Tif Lab, Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, 20133, Milan, Italy
5
Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
6
Dipartimento di Fisica G. Occhialini, U2, Università degli Studi di Milano-Bicocca, Piazza della Scienza, 3, 20126, Milan, Italy
7
INFN, Sezione di Milano-Bicocca, 20126, Milan, Italy
8
DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
* e-mail: stefano.forte@mi.infn.it
Received:
1
July
2019
Accepted:
16
October
2019
Published online:
15
November
2019
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.
© The Author(s), 2019
