The axion electromagnetic anomaly induces an oscillating electric dipole for any static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low-energy theorem which is a consequence of the spacetime-dependent cosmic background field of the axion in the limit that it is only locally time dependent (→v/c=0). The electron will acquire an oscillating electric dipole of frequency mₐ and strength ~10^-32 e-cm, 2 orders of magnitude above the nucleon, and within 4 orders of magnitude of the present standard model limit on a constant electron electric dipole moment. This may suggest sensitive new experimental venues for the axion dark-matter search.
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Christopher T. Hill (2015) studied this question.
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