Comment on "Axion induced oscillating electric dipole moments"

TL;DR

This paper critiques a previous claim by demonstrating that, under proper analysis, the axion electromagnetic anomaly does not induce an electron electric dipole moment, but oscillating EDMs in atoms and molecules arise from different mechanisms.

Contribution

The paper provides a corrected theoretical analysis showing no electron EDM induced by axions in the specified limit, clarifying the mechanisms behind oscillating EDMs.

Findings

No electron EDM induced by axions in the zero-velocity limit

Oscillating EDMs in atoms and molecules originate from different mechanisms

Clarifies the theoretical understanding of axion-induced electromagnetic effects

Abstract

In the recent work [Phys. Rev. D 91, 111702(R) (2015)], C. Hill concludes that the axion electromagnetic anomaly induces an oscillating electron electric dipole moment of frequency $m_a$ and strength $\sim 10^{-32}~e$ cm, in the limit $v/c \to 0$ for the axion field. Here, we demonstrate that a proper treatment of this problem in the lowest order yields $\textit{no}$ electric dipole moment of the electron in the same limit. Instead, oscillating electric dipole moments of atoms and molecules are produced by different mechanisms.