Towards the NNLO evolution of polarised parton distributions

TL;DR

This paper presents the first calculation of the polarized structure function g_1 at three-loop order in massless perturbative QCD, advancing the understanding of polarized parton distributions and their evolution.

Contribution

It provides the first NNLO polarized splitting functions Delta P_qq and Delta P_qg, extending previous two-loop results and confirming known coefficient functions.

Findings

Confirmed two-loop coefficient functions for polarized DIS.

Extracted NNLO polarized splitting functions Delta P_qq and Delta P_qg.

Revealed features related to sum rules and behavior at x→0 and x→1.

Abstract

We report on the first calculation of the structure function g_1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised cases of F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order (NNLO) quark-quark and gluon-quark splitting functions Delta P_qq and Delta P_qg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x to 1 and x to 0.