NNLO Time-like Splitting Functions in QCD

TL;DR

This paper reviews the calculation of time-like splitting functions in QCD at NNLO, highlighting recent progress in deriving these functions for quark-quark and gluon-gluon channels using space-like and time-like process relations.

Contribution

It presents the first complete three-loop results for quark-quark and gluon-gluon time-like splitting functions in perturbative QCD.

Findings

Quark-quark and gluon-gluon splitting functions obtained to three loops.

Relations between space-like and time-like processes used to derive functions.

Remaining unknowns are the quark-gluon and gluon-quark splitting functions beyond second Mellin moments.

Abstract

We review the status of the calculation of the time-like splitting functions for the evolution of fragmentation functions to the next-to-next-to-leading order in perturbative QCD. By employing relations between space-like and time-like deep-inelastic processes, all quark-quark and the gluon-gluon time-like splitting functions have been obtained to three loops. The corresponding quantities for the quark-gluon and gluon-quark splitting at this order are presently still unknown except for their second Mellin moments.