A calculation of the three-loop helicity-dependent splitting functions in QCD

TL;DR

This paper presents a comprehensive calculation of three-loop polarized splitting functions in QCD, providing essential NNLO corrections for polarized parton distribution evolution, with results indicating small corrections even at high coupling constants.

Contribution

The first complete calculation of three-loop polarized splitting functions in QCD, including previously missing components, advancing precision in polarized parton distribution evolution.

Findings

NNLO corrections are small even at large alpha_s

Complete matrix of polarized splitting functions calculated

New determination of previously missing splitting functions

Abstract

We have calculated the complete matrix of three-loop helicity-difference (`polarized') splitting functions Delta P_ik^(2), i,k = q,g, in massless perturbative QCD. In this note we briefly discuss some properties of the polarized splitting functions and our non-standard determination of the hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The resulting next-to-next-to-leading order (NNLO) corrections to the evolution of polarized parton distributions are illustrated and found to be small even at rather large values of the strong coupling constant alpha_s.