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<p>We present the complete 4-loop renormalisation of an Abelian chiral gauge theory in the Breitenlohner-Maison / ‘t Hooft-Veltman (BMHV) scheme. Employing a non-anticommuting <i>γ</i><sub>5</sub> in dimensional regularisation, we determine the full set of symmetry restoring counterterms from the quantum action principle. Our calculation represents the highest-order application of the BMHV framework so far, pushing the limits of a self-consistent treatment of <i>γ</i><sub>5</sub> at the multi-loop level. We describe the computational setup that we developed to perform the computations and discuss key implementation aspects, such as the BMHV algebra and tensor reduction. Our work demonstrates the feasibility of applying the BMHV scheme at high loop orders and establishes a solid foundation for future studies of high-precision electroweak physics.</p>

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Four-loop renormalisation of chiral gauge theories with non-anticommuting γ5 in the BMHV scheme

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月12日

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  • Andreas von Manteuffel,
  • Dominik Stöckinger,
  • Matthias Weißwange

摘要

We present the complete 4-loop renormalisation of an Abelian chiral gauge theory in the Breitenlohner-Maison / ‘t Hooft-Veltman (BMHV) scheme. Employing a non-anticommuting γ5 in dimensional regularisation, we determine the full set of symmetry restoring counterterms from the quantum action principle. Our calculation represents the highest-order application of the BMHV framework so far, pushing the limits of a self-consistent treatment of γ5 at the multi-loop level. We describe the computational setup that we developed to perform the computations and discuss key implementation aspects, such as the BMHV algebra and tensor reduction. Our work demonstrates the feasibility of applying the BMHV scheme at high loop orders and establishes a solid foundation for future studies of high-precision electroweak physics.