Three-loop calculations in non-Abelian gauge theories

TL;DR

This paper details a method for three-loop calculations in non-Abelian gauge theories, providing explicit results for QCD charge renormalization and anomalous dimensions, and exploring effects in supersymmetric models.

Contribution

It introduces a comprehensive analytical method for three-loop calculations in non-Abelian gauge theories, including explicit formulas and techniques for evaluating renormalization group functions.

Findings

Calculated three-loop charge renormalization function for QCD

Derived anomalous dimensions at three-loop level

Found charge renormalization effects vanish in SU(4)-supersymmetric models

Abstract

A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations have been published by the present authors (with A.Yu., Zharkov and L.V., Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, has also been published in 1980 as the JINR Communication E2-80-483.