Infrared regularization of non-Abelian gauge theories

TL;DR

This paper analyzes a BRS-invariant action for non-Abelian gauge theories with a mass term, showing consistent renormalization and separation of infrared and ultraviolet divergences despite the non-nilpotency of the BRS operator.

Contribution

It introduces a generalized Zinn-Justin equation for a non-nilpotent BRS operator, enabling consistent infrared regularization and renormalization in massive non-Abelian gauge theories.

Findings

Renormalization constants relations derived in dimensional regularization

Infrared singularities separated from ultraviolet infinities

New symmetries characterize physical operators and gauge dependence

Abstract

Curci and Ferrari found a unique BRS-invariant action for non-Abelian gauge theories which includes a mass term for the gauge bosons. I analyze this action. While the BRS operator is not nilpotent, the Zinn-Justin equation generalizes in a simple way so that the renormalization of the theory is consistent with the infrared regularization provided by the mass---infrared singularities and ultraviolet infinities are therefore clearly separated. Relations between renormalization constants are derived in dimensional regularization with minimal subtraction. Additional new symmetries allow a simple characterization of physical operators. A new formula is given for the gauge parameter dependence of physical operators.