Speaker
Description
The computation of high-precision electroweak observables is of growing importance to meet the stringent requirements of current and future experiments and to probe physics beyond the Standard Model (SM). Such computations inevitably encounter the $\gamma_5$-problem. The Breitenlohner-Maison/'t~Hooft-Veltman (BMHV) scheme provides the only known framework for treating $\gamma_5$ in dimensional regularisation (DReg) that is rigorously established to all orders. In this talk, I review the BMHV scheme along with the complications arising from the regularisation-induced breaking of BRST invariance and report on recent progress in the systematic renormalisation of chiral gauge theories within this framework. First, the multi-loop application of the BMHV scheme to an Abelian chiral gauge theory is presented up to the 4-loop level. Second, I discuss the BMHV renormalisation of the SM, including a complete 1-loop analysis, the implications of evanescent gauge interactions, and initial steps towards the 2-loop renormalisation.