Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting $\gamma_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

TL;DR

This paper extends the application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting $ ext{γ}_5$ to two-loop calculations in an abelian chiral gauge theory, identifying symmetry-restoring counterterms and UV divergences.

Contribution

It provides the full two-loop structure of symmetry-restoring counterterms and demonstrates a methodology applicable to nonabelian gauge theories.

Findings

Symmetry-restoring counterterms at two loops have the same structure as at one loop.

Ultraviolet divergences cannot be fully canceled by standard counterterms.

Identified UV divergent evanescent counterterms necessary for renormalization.

Abstract

We apply the BMHV scheme for non-anticommuting $\gamma_5$ to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.