Noncommutative QED and the lifetimes of ortho- and para-positronium

We examine the implications of including corrections associated with the noncommutative extension of quantum electrodynamics—NCQED—to the decays of the ortho- and para-positronium ( 3Ps and 1Ps) ground states. In NCQED, the well-known charge conjugation argument restricting 3Ps decays to an odd number of photons and 1Ps decays to an even number of photons no longer obtains. Instead, the dominant two photon decay mode of 1Ps is accompanied by a three photon mode. The dominant three photon decay mode of 3Ps receives a NCQED correction, but there is no corresponding two photon decay mode in the weak binding limit. These corrections to the Ps three photon decay mode have a different energy distribution, but their effect is too small to explain any discrepancy between the observed and calculated values of the 3Ps lifetime.