Anomaly Cancellation in Effective Field Theories From the Covariant Derivative Expansion

TL;DR

This paper extends a formalism for calculating anomalies in effective field theories, demonstrating that certain operators do not introduce new anomaly constraints in the Standard Model EFT.

Contribution

It generalizes the anomaly calculation method to include a broad class of operators, confirming their irrelevance to anomaly constraints in EFTs.

Findings

Operators with scalar, vector, tensor couplings do not produce relevant anomalies.

Anomaly cancellation conditions remain unchanged for the Standard Model EFT.

The formalism confirms the absence of new anomaly constraints from these operators.

Abstract

We extend our recently-proposed formalism for calculating anomalies of global and gauge symmetries using the Covariant Derivative Expansion to include a general class of operators that can appear in relativistic Effective Field Theories (EFTs). This allows us to prove that EFT operators involving general scalar, vector, and tensor couplings to fermion bilinears only give rise to irrelevant anomalies, which can be removed by an appropriate choice of counterterms, thereby confirming the absence of new constraints from anomaly cancellation on the Standard Model EFT.