Reply to "Comment on `Axion induced oscillating electric dipole moments' " [1]

TL;DR

This paper refutes a previous claim that axion interactions do not induce oscillating electric dipole moments, demonstrating a non-zero amplitude that leads to observable electric dipole radiation from electrons in a cosmic axion field.

Contribution

It provides a corrected calculation showing that axion interactions can produce observable oscillating electric dipole moments, countering prior assertions of their absence.

Findings

Non-zero amplitude for axion-induced electric dipole moments.

Electric dipole radiation can be emitted by electrons in a cosmic axion background.

The previous vanishing result was due to a misunderstanding of gauge and physics choices.

Abstract

We respond to a paper of Flambaum, et.al. [Phys. Rev. D95, no. 5, 058701 (2017)], claiming there is no effective induced oscillating electric dipole moment, e.g., for the electron, arising from interaction with an oscillating cosmic axion background via the anomaly. The relevant Feynman amplitude, Fig.(1), as computed by Flambaum et.al., becomes a total divergence, and vanishes. Contrary to this result, we obtained a nonvanishing amplitude, that yields physical electric dipole radiation for an electron (or any magnetic dipole moment) immersed in a cosmic axion field. We argue that the Flambaum et.al. counter-claim is incorrect, and is based upon a misunderstanding of a physics choice vs. gauge choice, and an assumption that electric dipoles be defined only by coupling to static (constant in time) electric fields.