• Accepted Paper

Four-loop nonsinglet splitting functions in QCD

Thomas Gehrmann, Andreas von Manteuffel, Vasily Sotnikov, and Tong-Zhi Yang

Phys. Rev. Lett. - Accepted 13 August, 2026

DOI: https://doi.org/10.1103/sgtd-c4zg

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.

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