The Path to N^3LO Parton Distributions
arxiv(2024)
摘要
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
(aN^3LO). We construct an approximation to the N^3LO 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 N^3LO corrections to
deep-inelastic scattering structure functions and extend the FONLL general-mass
scheme to 𝒪( α_s^3) accuracy. We determine a set of
aN^3LO PDFs by accounting both for the uncertainty on splitting functions due
to the incomplete knowledge of N^3LO 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^3LO PDFs from the MSHT group. We examine the
phenomenological impact of aN^3LO corrections on parton luminosities at the
LHC, and give a first assessment of the impact of aN^3LO PDFs on the Higgs
and Drell-Yan total production cross-sections. We find that the aN^3LO
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.
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