Axion EFT in the BMHV Scheme: Flavor Currents, Evanescent Operators and 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 $γ_5$ 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 $\mathcal{O}(α_s^2)$, 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.

Figures (5)

• Figure 1: Blob represents the tree-level operator insertion.
• Figure 2: Diagrams at one-loop, cross represents current insertion.
• Figure 3: Fermion self-energy diagrams at $\mathcal{O}(\alpha_s^2)$
• Figure 4: Crosses indicate current insertions; bracketed numbers show the total possible diagrams for that topology (e.g., J2 represents one of three).
• Figure 5: Crosses represent evanescent operator insertion, where 'EG' and 'EK' imply gluonic and kinetic evanescent insertion.