Dark Photon Decay Beyond The Euler-Heisenberg Limit

We calculate the exact width for a dark photon decaying to three photons at one loop order for dark photon masses m' below the e+e- production threshold of 2m_e. We find substantial deviations from previous results derived from the lowest order Euler-Heisenberg effective Lagrangian in the range m_e < m' < 2m_e, where higher order terms in the derivative expansion are nonnegligible. This mass range is precisely where the three photon decay takes place on cosmologically relevant timescales. Our improved analysis opens a window for dark photons in the range 850 keV < m' < 2m_e, 10^-5 < epsilon < 10^-4.