Symmetry-restoring finite counterterms of SMEFT four-fermion operator insertions at one loop

TL;DR

This paper calculates finite counterterms in SMEFT four-fermion operators at one loop within a specific regularization scheme, ensuring gauge symmetry is preserved and paving the way for higher-order computations.

Contribution

It identifies all finite counterterms needed to restore Slavnov-Taylor identities for dimension-6 four-fermion operators in the Breitenlohner-Maison scheme at one loop, a novel step in SMEFT calculations.

Findings

Finite counterterms restore gauge identities.

No obstructions to Slavnov-Taylor identities found.

Method simplifies calculations of finite effects.

Abstract

Some effects induced by SMEFT operators at one loop have attracted a lot of attention in recent years, in particular, the renormalization of divergences by physical operators in single insertions of dimension-6 operators. Important non-logarithmically enhanced contributions must also be calculated. We discuss dimensional regularization in the Breitenlohner-Maison-'t Hooft-Veltman scheme. The goal here consists of determining in this scheme quantum effects in chiral theories at one loop. Namely, the determination of finite counterterms at one loop that reestablish the Slavnov-Taylor identities, which follow from gauge symmetries. These counterterms are necessary due to the presence of evanescent symmetry-breaking terms in the classical Lagrangian needed to regularize fermion propagators. We consider a technique that allows an easier calculation of such finite effects, relying on the identification of $(D-4)/(D-4)$ terms of one-loop amplitudes with an external ghost leg. We focus on dimension-6 four-fermion operators, identifying all finite counterterms in the Breitenlohner-Maison-'t Hooft-Veltman scheme at one loop, and as expected find no obstructions to the Slavnov-Taylor identities that cannot be cured by finite counterterms. This represents one step towards moving to higher order calculations.