Effective Single Photon Decay Mode of Positronium Decay via Electroweak Interactions

We consider the decay of positronium to a neutrino-antineutrino accompanied by a single photon. Since the neutrino pair go undetected, this appears as a single photon decay of positronium. These decay channel are mediated through the exchange of the massive $W$ and $Z$ vector bosons of the electroweak interaction. After summing over the various neutrino channels, the standard model calculation yields the rate for such a single photon decay process of $\Gamma_{Ps \rightarrow \gamma}$ = 1.72 $\times 10^{-19}$ s$^{-1}$.