Abstract
In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/’t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the γ5-matrix appearing in gauge interactions is a non-anticommuting object, leading to a breaking of gauge and BRST invariance. Employing an efficient method based on the quantum action principle, we obtain the complete three-loop counterterm action which serves both to render the theory finite and to restore gauge and BRST invariance. The UV singular counterterms involve not only higher order ϵ-poles but also new counterterm structures emerging at the three-loop level for the first time; the finite symmetry-restoring counterterms are restricted to the same structures as at lower loop orders, just with different coefficients, aligning with our expectations. Both the singular and the finite counterterms include structures which cannot be obtained by the standard multiplicative renormalisation. Our results demonstrate that a rigorous treatment of chiral gauge theories with γ5 defined in the BMHV scheme at the multi-loop level is possible and that the obtained counterterm action is suitable for computer implementations, allowing automated calculations without ambiguities caused by γ5.
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Acknowledgments
D.S. and M.W. acknowledge financial support by the German Science Foundation DFG, grant STO 876/8-1. In particular, we would like to thank Vladyslav Shtabovenko not only for maintaining and developing the software FeynCalc and FeynHelpers, but also for many useful discussions that helped in developing the computational setup for evaluating the Feynman diagrams in this research work. We also want to thank our collaborators Hermes Belusca-Maito, Amon Ilakovac, Paul Kuhler and Marija Mađor-Božinović for insightful ideas and valuable discussions. Further, we would like to thank Konstantin Chetyrkin, Michal Czakon, Andreas Maier, Andreas von Manteuffel, Peter Marquard, York Schroder and Max Zoller for useful discussions and intellectual exchange. We are grateful to the Centre for Information Services and High Performance Computing [Zentrum fur Informationsdienste und Hochleistungsrechnen (ZIH)] TU Dresden for providing its facilities for high-performance calculations.
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Stöckinger, D., Weißwange, M. Full three-loop renormalisation of an abelian chiral gauge theory with non-anticommuting γ5 in the BMHV scheme. J. High Energ. Phys. 2024, 139 (2024). https://doi.org/10.1007/JHEP02(2024)139
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DOI: https://doi.org/10.1007/JHEP02(2024)139