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 ∼(few )×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, ∂_ta (t )∝m_a→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-Schrödinger nonrelativistic 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.