Towards the ${\mathrm{N^3LO}}$ evolution of parton distributions

Abstract

We present a brief status report on calculations for the four-loop splitting functions in perturbative QCD, which will pave the way to future determination of N 3 LO parton distribution functions of hadrons. In the large-N c limit, the exact four-loop contribution to the flavour non-singlet splitting functions has been obtained. For the remaining large-N c suppressed terms, we provide approximate expressions that are sufficient for phenomenological applications.