One-Loop Renormalization of Non-Abelian Gauge Theory and \beta Function Based on Loop Regularization Method

TL;DR

This paper computes one-loop renormalization constants for non-Abelian gauge theories using a symmetry-preserving loop regularization method, confirming known beta functions and maintaining original symmetries and divergences.

Contribution

It introduces and applies a novel loop regularization method that preserves symmetries and divergences in non-Abelian gauge theories at one-loop level.

Findings

Renormalization constants satisfy Ward-Takahashi-Slavnov-Taylor identities.

The method reproduces the well-known one-loop beta function for QCD.

The regularization maintains original divergences with two energy scales.

Abstract

All one-loop renormalization constants for Non-Abelian gauge theory are computed in details by using the symmetry-preserving Loop Regularization method proposed in\cite{LR1,LR2}. The resulting renormalization constants are manifestly shown to satisfy Ward-Takahaski-Slavnov-Taylor identities, and lead to the well-known one loop $\beta$ function for Non-Abelian gauge theory of QCD\cite{GWP}. The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit Check of those identities provides a clear demonstration how the symmetry-preserving Loop Regularization method can consistently be applied to non-Abelian gauge theories.