Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting $\gamma_5$

Abstract

We present a systematic functional approach to calculating symmetry-restoring counterterms in Effective Field Theories (EFTs) regulated using the Breitenlohner--Maison--'t Hooft--Veltman (BMHV) scheme. Building on a recently developed method that employs auxiliary spurion fields, our approach automates the extraction of these counterterms directly from the one-loop effective action, offering a streamlined and efficient procedure. We demonstrate its efficacy by applying it to the Standard Model Effective Field Theory (SMEFT) at dimension six, providing the first complete determination of its symmetry-restoring counterterms in the BMHV scheme. Our work establishes a robust foundation for consistent one-loop matching and two-loop running computations in EFTs with chiral gauge symmetries.