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

TL;DR

This paper reports recent advances in calculating higher-order splitting functions and cusp anomalous dimensions in perturbative QCD, including four-loop and five-loop results that improve the precision of parton distribution evolution.

Contribution

It provides the first four-loop (N^3LO) results for flavor-singlet splitting functions and the gluon cusp anomalous dimension, and initial five-loop (N^4LO) moments for non-singlet splitting functions.

Findings

Four-loop (N^3LO) flavor-singlet splitting functions computed.

Four-loop gluon cusp anomalous dimension calculated.

Initial five-loop (N^4LO) moments for non-singlet splitting functions obtained.

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.