Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

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.

Automated summary

The study applies the BMHV scheme to investigate an abelian chiral gauge theory with non-anticommuting gamma(5) at the two-loop level. The full structure of symmetry-restoring counterterms up to the two-loop level is determined, revealing that ultraviolet divergences cannot be completely canceled by counterterms generated by field and parameter renormalization. Additionally, the paper establishes a two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings, which can also be applied to nonabelian gauge theories.