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

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.

32 pages; v2: references added, minor typos corrected. Formatted for JHEP submission

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• A step towards a consistent treatment of chiral theories at higher loop order: the abelian case
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
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• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$