Renormalization of the axial current operator in dimensional regularization at four-loop in QCD

TL;DR

This paper calculates the four-loop renormalization constants for axial current operators in QCD using dimensional regularization, addressing the non-anticommuting gamma_5 and enabling precise extraction of mass logarithms.

Contribution

It provides the first four-loop renormalization constants for both singlet and non-singlet axial currents in QCD with a non-anticommuting gamma_5.

Findings

Renormalization constants determined up to four loops.

Application to non-decoupling mass logarithms in axial form factors.

Addresses gamma_5 issues in dimensional regularization.

Abstract

We provide the renormalization constants of the axial current operators, both singlet and non-singlet, in dimensional regularization up to four-loop order in QCD, determined using the off-shell Ward-Takahashi identity for an axial current with a non-anticommuting $\gamma_5$. A possible application of the result for the singlet axial current operator is the extraction of the non-decoupling mass logarithms in the axial quark form factors.