Chirality and parity violation are fundamental properties of nature. Regularization of chiral gauge theories like the electroweak SM entails difficulties since gauge invariance may not be manifestly preserved by the regularization scheme. In the context of dimensional regularization many variants of schemes for the treatment of gamma5 were proposed, many of which have the character of "recipes" which work and are efficient in specific, limited contexts but not in general. We propose a no-compromise approach using the BMHV scheme for gamma5. This scheme is known to be mathematically consistent at all orders, but it involves non-anticommuting gamma5 and breaks gauge invariance. We will specify in detail what that means for practical calculations at the one-loop and two-loop level. (based on https://inspirehep.net/literature/1793587 and further calculations)
At the end of the talk, if time permits, we will comment on another topic: the new result of the Fermilab g-2 measurement and its interpretation in terms of BSM scenarios.
With support from FCT through project UIDB/00777/2020