POSITRONIUM DECAY: GAUGE INVARIANCE AND ANALYTICITY

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wave function are removed. Nonfactorizable amplitudes are naturally introduced. Their dynamics are described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those nonfactorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of O(alpha(3)). Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.