Four-loop results on anomalous dimensions and splitting functions in QCD

TL;DR

This paper presents four-loop calculations of anomalous dimensions and splitting functions in QCD, achieving high precision results that enhance understanding of parton evolution and are relevant for high-accuracy phenomenology.

Contribution

It provides the first four-loop (N^3LO) results for non-singlet splitting functions in the planar limit and approximate expressions for the remaining parts, including cusp and virtual anomalous dimensions.

Findings

Achieved below 1% accuracy for non-singlet quark distribution evolution.

Obtained exact four-loop contributions in the planar limit.

Provided phenomenologically sufficient approximations for unknown parts.

Abstract

We report on recent progress on the flavour non-singlet splitting functions in perturbative QCD. The~exact four-loop (N^3LO) contribution to these functions has been obtained in the planar limit of a large number of colours. Phenomenologically sufficient approximate expressions have been obtained for the parts not exactly known so far. Both cases include results for the four-loop cusp and virtual anomalous dimensions which are relevant well beyond the evolution of non-singlet quark distributions, for which an accuracy of (well) below 1% has now been been reached.