Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting $γ_5$

TL;DR

The paper tackles the challenge of restoring gauge symmetry in chiral EFTs regulated with the mathematically consistent BMHV scheme, where the regularization induces explicit symmetry breaking via evanescent sectors. It develops a functional approach that uses auxiliary spurions to track and extract finite symmetry-restoring counterterms directly from the one-loop effective action, avoiding pre-specified operator bases. Applied to the SMEFT at dimension six, the method delivers the first complete set of one-loop symmetry-restoring counterterms, enabling consistent matching and paving the way for two-loop running in chiral gauge EFTs. The work introduces a Matchete-based automation pipeline, enhancing precision SMEFT computations and offering a robust framework for future NLO analyses and phenomenological studies in Higgs and electroweak observables.

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.

Figures (1)

• Figure 1: Left: Functional graph representing a contribution to the spurion-dependent part of the quantum effective action. The black dot denotes the effective vertex from $\mathcal{O}_{HW}$. Right: The same functional graph but with the $X$ and $\Delta$ terms replaced by their expressions in (\ref{['eq:ExXterms']},\ref{['eq:ExDeltaterms']}).