09 9 v 1 10 A ug 2 00 0 SLAC - PUB - 8557 hep - ph / 0008099 O ( α 3 ln α ) corrections to positronium decay rates

Positronium decays into two and three photons provide an interesting test of bound states Quantum Electrodynamics (QED). While the parapositronium (p-Ps) decay rate is well described by QED, it is known that the decay of orthopositronium (o-Ps) into three photons is still a controversial issue [1]. However, on the theoretical side there has been a major breakthrough recently and both decay rates are now known with O(α2) accuracy [2,3]. The next level of precision, i.e. O(α3) correction, is currently beyond the reach, although parts of the O(α3) correction that are enhanced by the logarithms of the fine structure constant, can be computed. The knowledge of these corrections is not of significant phenomenological importance at present since they are much smaller than the experimental accuracy for both p-Ps and o-Ps decays. Nevertheless, from a theoretical viewpoint, it is an interesting problem because at order α there are both leadingO(α3 lnα) and subleading O(α3 lnα) corrections. The calculation of the leading O(α3 ln α) corrections is a fairly simple enterprise; it has been done quite some time ago [4]. Here we are interested in subleading logarithmic corrections. In order to compute them, we utilize the nonrelativistic QED in dimensional regularization and we explain how in this framework the logarithmic corrections can be computed using limited amount of information. Before diving into the description of the calculation, let us summarize our results. For the O(α3 lnα) corrections to paraand orthopositronium decay rates we find: