Spurious gauge-invariance and $\gamma_5$ in Dimensional Regularization

TL;DR

This paper addresses the $ ext{γ}_5$ problem in dimensional regularization for chiral gauge theories by introducing auxiliary fields to restore a spurious gauge invariance, simplifying calculations and symmetry constraints.

Contribution

It proposes a novel method using auxiliary fields and the background field method to restore gauge invariance in dimensional regularization for chiral theories, improving upon existing schemes.

Findings

Counterterms at 1-loop are explicitly evaluated for the Standard Model.

The approach constrains counterterms through formal covariance and symmetries.

The method simplifies handling of chiral gauge theories in dimensional regularization.

Abstract

Dimensional regularization is arguably the most popular and efficient scheme for multi-loop calculations. Yet, when applied to chiral (gauge) theories like the Standard Model and its extensions, one is forced to deal with the infamous "$\gamma_5$ problem". The only formulation that has been demonstrated to be consistent at all orders in perturbation theory, known as Breiteinlhoner-Maison-'t Hooft-Veltman scheme, is rather cumbersome because of the lack of manifest chiral gauge-invariance. In this paper we point out that this drawback can be alleviated by the introduction of auxiliary fields that restore a spurious version of gauge-invariance. If combined with the background field method, all 1PI amplitudes and the associated counterterms are formally covariant and thus severely constrained by the symmetries. As an illustration we evaluate the symmetry-restoring counterterms at 1-loop in the most general renormalizable gauge theory with Dirac fermions and scalar fields, the Standard Model representing a particular example.