Renormalization of the flavor-singlet axial-vector current and its anomaly 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 $[F\tilde{F}{]}_R$ and that of ${\alpha }_s$ is verified explicitly to hold true at 4-loop order.

Comments: Contribution to the Proceedings of the 15th International Symposium on Radiative Corrections (RADCOR) and the XIX Workshop on Radiative Corrections for the LHC and Future Colliders (LoopFest), 2021