The path to N3LO parton distributions

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 (aN3 LO). We construct an approximation to the N 3 LO 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 N3 LO corrections to deep-inelastic scattering structure functions and extend the
FONLL general-mass scheme to O (α3s) accuracy. We determine a set of aN 3 LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N3 LO 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 aN 3 LO PDFs from the MSHT group. We examine the phenomenological impact of aN 3 LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN 3 LO PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the aN 3 LO 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.