Additional moments and x-space approximations of four-loop splitting functions in QCD

TL;DR

This paper extends the calculation of four-loop splitting functions in QCD to higher moments, providing approximations that enable more accurate N^3LO evolution of parton distributions, especially outside small-x regions.

Contribution

It presents extended moments of four-loop splitting functions and constructs approximations for uncomputed cases, aiding higher-order QCD calculations.

Findings

Extended moments up to N=12 for pure-singlet quark case.

Constructed approximations for quark-gluon and gluon-gluon splitting functions.

Provided new large-x results for gluon-gluon splitting functions.

Abstract

We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical quantities in inclusive deep-inelastic scattering, have been and will be used to validate conceptionally much more challenging determinations of these splitting functions from off-shell operator matrix elements (OMEs). For the quark-gluon and gluon-gluon splitting functions, which have yet to be computed to higher N using OMEs, we construct approximations based on our moments and endpoint constraints, where we present new large-x results for the gluon-gluon case. These approximations facilitate an approximate N^3LO evolution of parton distributions which are sufficiently accurate outside the region of small momentum fractions x.