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

TL;DR

This paper introduces an automated method for calculating symmetry-restoring counterterms in EFTs regulated with the BMHV scheme, demonstrated on SMEFT at dimension six, enabling consistent loop computations.

Contribution

It develops a systematic, automated approach using auxiliary spurion fields to extract counterterms directly from the one-loop effective action in EFTs.

Findings

First complete determination of SMEFT counterterms in BMHV scheme

Streamlined procedure for symmetry restoration in chiral EFTs

Foundation for two-loop running calculations in SMEFT

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.