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

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.Comment: 11 pages, LaTeX (PoS style), 4 eps-figures. Contribution to the proceedings of `RADCOR 2017', St. Gilgen (Austria), September 201