The soft-energy region in the radiative decay of bound states Original Research Article

The orthopositronium decay to three photons is studied in the phase-space region where one of the photons has an energy comparable to the relative three-momentum of the image system (image). The NRQED computation in this regime shows that the dominant contribution arises from distances image, which allows to treat the Coulomb interaction perturbatively. The small-photon energy expansion of the 1-loop decay spectrum from full QED yields the same result as the effective theory. By doing the threshold expansion of the 1-loop QED amplitude we confirm that the leading term arises from a loop-momentum region where image. This corresponds to a new non-relativistic loop-momentum region, which has to be taken into account for the description of a non-relativistic particle–antiparticle system that decays through soft photon emission.