Shedding Light on Evanescent Shadows -- Exploration of non-anticommuting $\gamma_5$ in Dimensional Regularisation

The mathematical consistency of the BMHV scheme of dimensional regularisation (DReg) comes at the cost of requiring symmetry-restoring counterterms to cancel the regularisation-induced breaking of gauge and BRST invariance. There is no unique way to extend a 4-dimensional theory to $D$ dimensions, and different choices can be made for the dimensionally regularised fermions, evanescent parts of their kinetic terms and evanescent gauge interactions. Here we present a detailed study of the impact of changing such evanescent details. We leverage this freedom to identify a particularly convenient formulation that simplifies practical calculations. In order to thoroughly study the available options, we focus on a general abelian chiral gauge theory including scalar fields and adopt a general approach to the BMHV implementation. This allows for specialisation to various models and different approaches, including those from the literature. Importantly, our model can be specialised to the abelian sector of the Standard Model (SM). Consequently, this article also serves as a roadmap for upcoming applications to the full SM.