Axion EFT in the BMHV Scheme: Flavor Currents, Evanescent Operators and Ward Identities

TL;DR

This paper systematically analyzes axion effective field theory within the BMHV scheme, focusing on renormalization, evanescent operators, and Ward identities, verified up to two-loop order.

Contribution

It provides a detailed framework for handling evanescent operators and Ward identities in axion EFT within the BMHV scheme, including explicit two-loop calculations.

Findings

Verified Ward identities up to two-loop order including finite terms

Identified how evanescent operators mix into physical operators

Determined finite renormalization needed to restore Ward identities

Abstract

We present a systematic analysis of axion effective field theory within the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) scheme, focusing on the renormalization of fermionic dimension-five operators and the associated chiral flavor currents. In this framework, the non-anticommuting nature of $\gamma_5$ in $d \neq 4$ dimensions leads to violations of naive Ward identities through the emergence of evanescent operators. We derive the bare and renormalized Ward identities for chiral currents, explicitly identifying the equation-of-motion and evanescent operator contributions. Using diagrammatic calculations, we verify the validity of these identities up to two-loop order $\mathcal{O}(\alpha_s^2)$, including both pole and finite terms. We demonstrate how evanescent operators mix into physical operators and determine the finite renormalization required to restore four-dimensional Ward identities, recovering the expected structure of axial current renormalization and the anomaly. Our results provide a consistent and transparent framework for multi-loop computations in axion EFT and highlight the essential role of evanescent operators in maintaining scheme consistency.