Anomalous dimensions of quark masses in the three-loop approximation

TL;DR

This paper computes the three-loop radiative corrections to quark mass renormalization constants in non-abelian gauge theories like QCD, providing detailed methods and results for anomalous dimensions using dimensional regularization.

Contribution

It presents the first detailed three-loop calculations of fermion mass anomalous dimensions in QED and QCD using dimensional regularization and the minimal subtraction scheme.

Findings

Three-loop anomalous dimensions for QED and QCD fermions.

Explicit expressions for the renormalization group function γ_m.

Use of computer algebra systems for complex calculations.

Abstract

The results of calculation of the three-loop radiative correction to the renormalization constant of fermion masses for non-abelian gauge theory interacting with fermions are presented. Dimensional regularization and the 't Hooft minimal subtraction scheme are used. The method of calculation is described in detail. The renormalization group function $\gamma_m$ determining the behavior of the effective mass of fermions is presented. The anomalous dimensions of fermions for QED and QCD up to three loops are given. All calculations were performed on a computer with the help of the SCHOOONSCHIP system for analytical manipulations. The present text was published in 1982 as a JINR Communication, JINR-P2-82-900 (in russian).