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Axion Induced Oscillating Electric Dipole Moment of the Electron

A cosmic axion, via the electromagnetic anomaly, induces an oscillating electric dipole for the electron of frequency $m_a$ and strength $\sim$(few)$\times 10^{-32}$ e-cm, two orders of magnitude above the nucleon, and within a few orders of magnitude of the present standard model constant limit. We give a detailed study of this phenomenon via the interaction of the cosmic axion, through the electromagnetic anomaly, with particular emphasis on the decoupling limit of the axion, $\partial_t a(t)\propto m_a \rightarrow 0$. The analysis is subtle, and we find the general form of the action involves a local contact interaction and a nonlocal contribution, analogous to the "transverse current" in QED, that enforces the decoupling limit. We carefully derive the effective action in the Pauli-Schroedinger non-relativistic formalism, and in Georgi's heavy quark formalism adapted to the "heavy electron" ($m_e>>m_a$). We compute the electric dipole radiation emitted by free electrons, magnets and currents, immersed in the cosmic axion field, and discuss experimental configurations that may yield a detectable signal.