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arXiv · 2609.38557

Symmetry-Restoring Counter-terms in Massive Gauge Theories with Non-Anticommuting $γ_5$ via Gauge-Invariant Sector Decomposition

Andrea Quadri
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Abstract

We compute the one-loop breaking of the Slavnov-Taylor (ST) identities in a massive Abelian chiral gauge theory with spontaneous symmetry breaking, regularized in the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) scheme. We also provide the one-loop finite counter-terms required to restore the one-loop ST identities. The recent formulation of spontaneously broken models based on the Fröhlich-Morchio-Strocchi (FMS) gauge-invariant and dynamical (i.e. propagating inside loops) fields is used. The proposed algebraic approach holds true to all orders in the loop expansion and allows for a consistent decomposition of the ST breaking into independent sectors. By using cohomological techniques we eventually constrain the dependence of the ST breaking on the vacuum expectation value of the Higgs field. This yields a set of differential equations that provide a useful check of the mass-dependent terms in the ST breaking terms in the broken phase. They can be generalized to the non-Abelian case, both in the gauge-invariant formalism and in the conventional one. In the massless limit we find agreement with previous calculations present in the literature.

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Andrea Quadri. 2026-10-10. Symmetry-Restoring Counter-terms in Massive Gauge Theories with Non-Anticommuting $γ_5$ via Gauge-Invariant Sector Decomposition. https://arxiv.org/abs/2609.38557

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