Towards three-loop QCD corrections to the time-like splitting functions

TL;DR

This paper discusses the progress towards calculating three-loop QCD corrections to time-like splitting functions, essential for understanding hadron production and parton evolution, through direct first-principles computation.

Contribution

It presents an independent approach to compute the three-loop time-like splitting functions, addressing gaps left by previous symmetry-based inferences.

Findings

Progress in computing three-loop corrections

Identification of unresolved parts in previous methods

Development of new computational tools

Abstract

We report on the status of a direct computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production and the evolution of the parton fragmentation distributions. Current knowledge about them at three loops has been inferred by means of crossing symmetry from their related space-like counterparts, which has left certain parts of the off-diagonal quark-gluon splitting function undetermined. This motivates an independent calculation from first principles. We review the tools and methods which are applied to attack the problem.