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<p>Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic <i>γ</i><sub>5</sub>-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.</p>

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Two-loop renormalization of a chiral SU(2) gauge theory in dimensional regularization with non-anticommuting γ5

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月4日

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  • Paul Kühler,
  • Dominik Stöckinger

摘要

Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic γ5-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.