Axion induced oscillating electric dipole moments

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 $(\overrightarrow{v}/c=0)$. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\sim {10}^{-32}\mathrm{e}\text{−}\mathrm{cm}$, 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.

Figure 1

Feynman diagram for axion induced electric dipole moment. Photon $q$ emitted from electron magnetic moment. Solid dot is the axion anomaly interaction, $\theta \overrightarrow{E}·\overrightarrow{B}$. Dashed line: incoming axion $\theta$, $p$. Outgoing photon: $p+q$, ${\epsilon }_{\mu }$. Solid line: incoming electron $k$; recoil electron, $k^{\prime }$.