Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ at the Multi-Loop Level
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911488550109184 |
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| author | Weißwange, Matthias |
| author_facet | Weißwange, Matthias |
| contents | This thesis presents a comprehensive study of the renormalisation of chiral gauge theories in dimensional regularisation (DReg) at the multi-loop level. We employ the mathematically consistent Breitenlohner-Maison/`t~Hooft-Veltman (BMHV) scheme with non-anticommuting $γ_5$, whose modified algebraic relations induce a spurious violation of gauge and BRST invariance. A central focus is the systematic restoration of the broken symmetry, for which we provide a transparent and fully algorithmic procedure based on the quantum action principle. A major achievement of this work is the complete 4-loop renormalisation of an Abelian chiral gauge theory -- the highest-order application of the BMHV scheme to date. This calculation is made possible by an automated, high-performance computational framework incorporating several optimised algorithms. Our results demonstrate that a rigorous, self-consistent treatment of $γ_5$ is feasible even at very high loop orders. We further analyse dimensional ambiguities and evanescent details corresponding to different implementations of the regularisation, and identify practically efficient prescriptions for $D$-dimensional fermions and gauge interactions. Building on these insights, we present the complete 1-loop renormalisation of the full Standard Model (SM) in the BMHV scheme, providing a first step towards a fully self-consistent multi-loop renormalisation of the SM and establishing a solid foundation for future high-precision electroweak phenomenology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ at the Multi-Loop Level Weißwange, Matthias High Energy Physics - Phenomenology High Energy Physics - Theory This thesis presents a comprehensive study of the renormalisation of chiral gauge theories in dimensional regularisation (DReg) at the multi-loop level. We employ the mathematically consistent Breitenlohner-Maison/`t~Hooft-Veltman (BMHV) scheme with non-anticommuting $γ_5$, whose modified algebraic relations induce a spurious violation of gauge and BRST invariance. A central focus is the systematic restoration of the broken symmetry, for which we provide a transparent and fully algorithmic procedure based on the quantum action principle. A major achievement of this work is the complete 4-loop renormalisation of an Abelian chiral gauge theory -- the highest-order application of the BMHV scheme to date. This calculation is made possible by an automated, high-performance computational framework incorporating several optimised algorithms. Our results demonstrate that a rigorous, self-consistent treatment of $γ_5$ is feasible even at very high loop orders. We further analyse dimensional ambiguities and evanescent details corresponding to different implementations of the regularisation, and identify practically efficient prescriptions for $D$-dimensional fermions and gauge interactions. Building on these insights, we present the complete 1-loop renormalisation of the full Standard Model (SM) in the BMHV scheme, providing a first step towards a fully self-consistent multi-loop renormalisation of the SM and establishing a solid foundation for future high-precision electroweak phenomenology. |
| title | Renormalisation of Chiral Gauge Theories with Non-Anticommuting $γ_5$ at the Multi-Loop Level |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.05059 |