# Dark Photon Decay Beyond The Euler-Heisenberg Limit

## TL;DR

This paper precisely calculates the decay width of dark photons into three photons for masses below the electron-positron threshold, revealing significant deviations from previous approximations and expanding the viable parameter space for dark photon detection.

## Contribution

It provides the exact decay width calculation for dark photons below 2m_e, improving upon previous Euler-Heisenberg-based estimates and identifying a broader parameter space for cosmologically relevant dark photons.

## Key findings

- Significant deviations from previous decay width estimates.
- Expanded viable mass range for dark photons to 850 keV - 2m_e.
- Dark photon decay timescales relevant for cosmology.

## Abstract

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.