Anomalous dimensions and splitting functions beyond the next-to-next-to-leading order

Abstract

We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, N^3LO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (N^4LO) non-singlet splitting functions.