Renormalization of the flavor-singlet axial-vector current and its anomaly in QCD

TL;DR

This paper computes the renormalization constant of the flavor-singlet axial-vector current in QCD to three-loop order and confirms the equality of related renormalization constants at four loops, advancing precision in quantum chromodynamics calculations.

Contribution

It provides the first three-loop calculation of the renormalization constant $Z_J$ with a non-anticommuting $oldsymbol{ extgamma_5}$ in dimensional regularization and verifies the four-loop equality of $Z_{F ilde{F}}$ and $oldsymbol{ extalpha_s}$ renormalization constants.

Findings

$Z_J$ determined to order $oldsymbol{ extalpha_s^3}$ in QCD.

Confirmed the equality of $Z_{F ilde{F}}$ and $oldsymbol{ extalpha_s}$ at four-loop order.

Enhanced the understanding of axial current renormalization in QCD.

Abstract

The renormalization constant $Z_J$ of the flavor-singlet axial-vector current with a non-anticommuting $\gamma_5$ in dimensional regularization is determined to order $\alpha_s^3$ in QCD with massless quarks. In addition, the equality between the $\overline{\mathrm{MS}}$ renormalization constant $Z_{F\tilde{F}}$ associated with the operator $\big[F \tilde{F} \big]_{R}$ and that of $\alpha_s$ is verified explicitly to hold true at 4-loop order.