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arXiv · 2406.17013

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

Pablo Olgoso Ruiz·Luca Vecchi
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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.

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Pablo Olgoso Ruiz, Luca Vecchi. 2024-06-24. Spurious gauge-invariance and $\gamma_5$ in Dimensional Regularization. https://arxiv.org/abs/2406.17013

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