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

TL;DR

This paper investigates the radiative decay of orthopositronium in a specific energy region, revealing a new non-relativistic loop-momentum region crucial for understanding soft photon emission in bound state decays.

Contribution

It identifies and analyzes a novel non-relativistic loop-momentum region affecting soft photon emission in bound state decays, confirmed through effective theory and threshold expansion methods.

Findings

Dominant contribution from distances ~ 1/(mw)^(1/2)

Perturbative treatment of Coulomb interaction in this regime

Confirmation of the leading term from a specific loop-momentum region

Abstract

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 e+e- system (w ~ m alpha). The NRQED computation in this regime shows that the dominant contribution arises from distances ~ 1/(mw)^(1/2), 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 q^0 ~ q^2/m ~ w. 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.