The four-loop non-singlet splitting functions in QCD
High Energy Physics - Phenomenology
2026-04-27 v2 High Energy Physics - Theory
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.
Cite
@article{arxiv.2604.09534,
title = {The four-loop non-singlet splitting functions in QCD},
author = {Thomas Gehrmann and Andreas von Manteuffel and Vasily Sotnikov and Tong-Zhi Yang},
journal= {arXiv preprint arXiv:2604.09534},
year = {2026}
}
Comments
10 pages, 3 figures, ancillary files with results; v2: added time-like splitting functions and comment on small-x limit