The four-loop non-singlet splitting functions in QCD

TL;DR

This paper presents the first complete analytic calculation of four-loop non-singlet splitting functions in QCD, enhancing precision in parton distribution evolution and resummation techniques.

Contribution

It provides the first fully analytic expressions for four-loop non-singlet splitting functions in QCD, confirming previous partial results and enabling improved theoretical predictions.

Findings

Confirmed previous partial results for four-loop splitting functions.

Derived fully analytic expressions for all non-singlet contributions at four loops.

Provided numerical representations suitable for practical parton evolution.

Abstract

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop splitting functions in perturbative QCD that control the evolution of quark non-singlet distributions. We confirm previous partial results and obtain, for the first time, fully analytic expressions for all non-singlet contributions at this order. These allow us to extract the analytic form of the four-loop virtual and rapidity anomalous dimensions entering logarithmic resummation. We provide precise numerical representations of the splitting functions suitable for parton evolution.