Spurious gauge-invariance and $γ_5$ in Dimensional Regularization
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909230587445248 |
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| author | Ruiz, Pablo Olgoso Vecchi, Luca |
| author_facet | Ruiz, Pablo Olgoso Vecchi, Luca |
| contents | 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 "$γ_5$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spurious gauge-invariance and $γ_5$ in Dimensional Regularization Ruiz, Pablo Olgoso Vecchi, Luca High Energy Physics - Phenomenology High Energy Physics - Theory 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 "$γ_5$ 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. |
| title | Spurious gauge-invariance and $γ_5$ in Dimensional Regularization |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.17013 |