Order ALPHA**2 Nonrelativistic Corrections to Positronium Hyperfine Splitting and Decay Rate Using Nonrelativistic Quantum Electrodynamics.

Positronium represents an ideal system for testing both quantum electrodynamics and two-body formalisms. Two of the most interesting positronium properties are the ground state hyperfine splitting of and the decay rate of the n = 1, S = 1 (orthopositronium) state. Unfortunately, because of the difficulties involved in the theoretical calculations, they are not yet precise enough to permit a meaningful comparison with the experimental values. The goal of this work was to reduce the theoretical uncertainty. We used an effective field theory (nonrelativistic quantum electrodynamics) to decouple the relativistic loop momenta (i.e. of order of the electron mass m) from non -relativistic ones (of order of the typical bound state momentum, malpha). We have computed the order alpha**2 nonrelativistic corrections to both the hyperfine splitting and the decay rate and show how the remaining (relativistic) contributions can be calculated in terms of conventional QED scattering amplitudes. Therefore, our calculation takes into account all binding effects. Using our results, the alpha**2 corrections can be completed without a priori knowledge of bound state physics.