The four-loop non-singlet splitting functions in QCD

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.

Comments: 10 pages, 3 figures, ancillary files with results; v2: added time-like splitting functions and comment on small-x limit