Advances at the $\gamma_5$-Frontier

TL;DR

This paper reviews progress in the dimensional renormalization of chiral gauge theories using the BMHV scheme with non-anticommuting $oldsymbol{ extgamma_5}$, focusing on symmetry restoration and multi-loop calculations.

Contribution

It provides a comprehensive overview of the BMHV scheme's methodology, recent multi-loop results, and potential applications to Standard Model-like theories.

Findings

Successful symmetry restoration procedures demonstrated

Multi-loop renormalization results for Abelian and non-Abelian theories presented

Insights into implementing BMHV in SM-like models discussed

Abstract

These proceedings discuss the current progress of the no-compromise approach to the dimensional renormalization of chiral gauge theories in the context of the BMHV scheme with non-anticommuting $\gamma_5$. Despite spuriously breaking BRST-invariance in intermediate steps, it is the only scheme which handles the well-known $\gamma_5$-problem mathematically consistently. We begin with a brief motivation, followed by an exposition of our methodology. Specifically, we illustrate the symmetry restoration procedure to obtain the required symmetry-restoring counterterms and provide insights into our computational setups, including recent developments. Building up on this, we present recent results and advances for the multi-loop renormalization of Abelian and non-Abelian chiral gauge theories, before concluding this article with a discussion on prospective implementations of the BMHV regularization in SM-like models.