  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.
