Two-Loop Renormalization of a Chiral $SU(2)$ Gauge Theory in Dimensional Regularization with Non-Anticommuting $γ_5$
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| Format: | Preprint |
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2025
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| _version_ | 1866908307229245440 |
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| author | Kühler, Paul Stöckinger, Dominik |
| author_facet | Kühler, Paul Stöckinger, Dominik |
| contents | Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic $γ_5$-matrix in Dimensional Regularization (DReg). In the all-order consistent BMHV scheme anticommutativity has to be sacrificed, resulting in spurious breakings of BRST invariance, the restoration of which necessitates finite, symmetry-restoring counterterms. Following recent advances in successfully applying this scheme to multi-loop calculations for Abelian models, we shall here present the first complete non-Abelian two-loop result for the case of $SU(2)$, which is of particular interest to the Standard Model. We provide the complete list of finite, two-loop symmetry restoring counterterms and discuss intricacies of the non-Abelian implementation. Except for one novel term, the finite counterterm action exhibits the same structure as at one-loop order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Loop Renormalization of a Chiral $SU(2)$ Gauge Theory in Dimensional Regularization with Non-Anticommuting $γ_5$ Kühler, Paul Stöckinger, Dominik High Energy Physics - Phenomenology High Energy Physics - Theory Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic $γ_5$-matrix in Dimensional Regularization (DReg). In the all-order consistent BMHV scheme anticommutativity has to be sacrificed, resulting in spurious breakings of BRST invariance, the restoration of which necessitates finite, symmetry-restoring counterterms. Following recent advances in successfully applying this scheme to multi-loop calculations for Abelian models, we shall here present the first complete non-Abelian two-loop result for the case of $SU(2)$, which is of particular interest to the Standard Model. We provide the complete list of finite, two-loop symmetry restoring counterterms and discuss intricacies of the non-Abelian implementation. Except for one novel term, the finite counterterm action exhibits the same structure as at one-loop order. |
| title | Two-Loop Renormalization of a Chiral $SU(2)$ Gauge Theory in Dimensional Regularization with Non-Anticommuting $γ_5$ |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.06080 |