Orthopositronium Decay Spectrum using NRQED

Abstract

As noticed in Ref.[1], the Ore-Powell's classical calculation of the o-Ps -> 3 gamma decay amplitude does not fulfill Low's theorem requirements for the low energy end of the photon spectrum. We reanalyze the implications of Low's theorem applied to this decay considering the interplay between the soft photon limit and the energy scales present in the e+e- system. For energetic photons, the spectrum agrees with the Ore-Powell result, but deviates from it when the photon energy is comparable to the positronium binding energy. In this region it is found that bound states effects are essential to reach agreement with Low's theorem and can be accounted for in the framework of non-relativistic QED.