Renormalization of the pseudoscalar operator at four loops in QCD

TL;DR

This paper computes the four-loop renormalization constant for the pseudoscalar operator in QCD with a non-anticommuting gamma_5, and predicts the five-loop MS-bar factor based on renormalization-group invariance.

Contribution

It provides the first four-loop calculation of the pseudoscalar operator renormalization constant and extends predictions to five loops in QCD.

Findings

Renormalization constant computed up to four loops.

Predicted five-loop MS-bar renormalization factor.

Enhanced precision for pseudoscalar operator in QCD.

Abstract

We present the renormalization constant of the pseudoscalar operator defined with a non-anticommuting $\gamma_5$ in dimensional regularization up to four-loop order in perturbative Quantum Chromodynamics (QCD). Furthermore, by virtue of renormalization-group invariance of the relation between the scalar and the pseudoscalar operator, we predict the $\overline{\mathrm{MS}}$ factor of the renormalization constant for the latter at five-loop order in QCD.