https://doi.org/10.1140/epjc/s10052-024-12891-7
Regular Article - Theoretical Physics
The path to 
parton distributions
1
The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd, EH9 3JZ, Edinburgh, Scotland
2
Tif Lab, Dipartimento di Fisica, Università di Milano, Milan, Italy
3
INFN, Sezione di Milano, Via Celoria 16, 20133, Milan, Italy
4
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
5
Department of Physics and Astronomy, Vrije Universiteit, 1081 HV, Amsterdam, The Netherlands
6
Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
7
Department of Physics, University of Jyvaskyla, P.O. Box 35, 40014, Jyvaskyla, Finland
8
Helsinki Institute of Physics, P.O. Box 64, 00014, Helsinki, Finland
9
DAMTP, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK
10
Dipartimento di Fisica, Università degli Studi di Torino, Turin, Italy
11
INFN, Sezione di Torino, Via Pietro Giuria 1, 10125, Turin, Italy
12
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074, Würzburg, Germany
Received:
1
March
2024
Accepted:
7
May
2024
Published online:
3
July
2024
We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (
). We construct an approximation to the splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to 
accuracy. We determine a set of PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the PDFs from the MSHT group. We examine the phenomenological impact of corrections on parton luminosities at the LHC, and give a first assessment of the impact of PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.
This paper is dedicated to the memory of Stefano Catani, Grand Master of QCD, great scientist and human being.
© The Author(s) 2024
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Funded by SCOAP3.
