Regularization of fermion loops in gauge models

Abstract

Fermion loops in gauge models with ${\ensuremath{\gamma}}_{5}$ couplings cannot be regularized in a gauge-invariant manner either by the method of auxiliary fields or by dimensional continuation. It is shown that in the absence of a gauge-invariant regularization procedure, the method of auxiliary fields can be employed in such a way that non-gauge-invariance is confined to the renormalization constants. It is thus possible to obtain gauge-invariant renormalized results as well as resolve anomalies without the use of Ward's identities. Explicit calculations are carried out for the self-energy and triangle diagrams with fermion loops in the Appelquist-Quinn model. The present treatment is also compared with naive dimensional regularization for the ${\ensuremath{\gamma}}_{5}$ couplings.