Axion Effective Action

TL;DR

This paper develops a systematic method for constructing effective field theories involving anomalous symmetries, focusing on axion models and addressing divergences in Goldstone boson couplings.

Contribution

It introduces a path integral approach to resolve divergences in EFTs with anomalous symmetries, applicable to axion and ALP models.

Findings

Reproduces non-intuitive axion-gauge field couplings

Provides a consistent formalism for EFTs with anomalies

Facilitates systematic axion and ALP searches

Abstract

In this paper, we discuss the construction of Effective Field Theories (EFTs) in which a chiral fermion, charged under both gauge and global symmetries, is integrated out. Inspired by typical axion models, these symmetries can be spontaneously broken, and the global ones might also be anomalous. In this context, particular emphasis is laid on the derivative couplings of the Goldstone bosons to the fermions, as these lead to severe divergences and ambiguities when building the EFT. We show how to precisely solve these difficulties within the path integral formalism, by adapting the anomalous Ward identities to the EFT context. Our results are very generic, and when applied to axion models, they reproduce the non-intuitive couplings between the massive SM gauge fields and the axion. Altogether, this provides an efficient formalism, paving the way for a systematic and consistent methodology to build entire EFTs involving anomalous symmetries, as required for axion or ALP searches.