The $\bar{\mathrm{MS}}$ renormalization constant of the singlet axial current operator at $\mathcal{O}(\alpha_s^5)$ in QCD

TL;DR

This paper calculates the five-loop order renormalization constant for the singlet axial current in QCD using advanced perturbative techniques and existing four-loop results, enhancing precision in theoretical predictions.

Contribution

It provides the first five-loop order $ar{\mathrm{MS}}$ renormalization constant for the singlet axial current in QCD, extending previous four-loop computations.

Findings

Five-loop order renormalization constant computed.

Utilizes Adler-Bell-Jackiw equation with renormalized operators.

Builds on previous four-loop diagrammatic results.

Abstract

We provide the $\bar{\mathrm{MS}}$ factor of the renormalization constant of the singlet axial-current operator in dimensional regularization at $\mathcal{O}(\alpha_s^5)$ in perturbative Quantum Chromodynamics (QCD). The result is obtained from a formula derived using the Adler-Bell-Jackiw equation in terms of renormalized operators. The required input consists of the complete four-loop results for operator renormalization constants obtained by explicit diagrammatic computation in a previous publication.