The Standard Model with Non-Anticommuting $γ_5$ in the BMHV Scheme

Abstract

The Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme provides a treatment of $γ_5$ in dimensional regularisation (DReg) that is guaranteed to be self-consistent at all orders, but it breaks gauge and BRST invariance at the regularised level, which must be restored by suitable counterterms. We present the complete 1-loop renormalisation of the full Standard Model in the BMHV scheme in general $R_ξ$-gauge, including all singular and all finite symmetry-restoring counterterms. We further analyse the impact of evanescent gauge interactions, which allow the photon and gluon currents to be treated either 4- or $D$-dimensionally. We show that QCD always contributes to the symmetry breaking, so that the Standard Model must be treated as a whole, and we recommend a purely 4-dimensional treatment of electroweak gauge interactions. Our results provide a necessary step towards multi-loop electroweak precision calculations with a fully consistent treatment of $γ_5$.