Relativistic effects in γγ decays of P-wave positronium and qq-bar systems

Theories of the two photon couplings of P-wave positronium and qq-bar systems are reviewed and a relationship is found between field theoretic calculations of qq-bar→γγ and the Vector Meson Dominance (VMD) model for both heavy and light quark systems. Relativistic corrections to the two photon decay rates are evaluated, and are found to be very important for the light quark system. We find that the widely quoted ratio of 15/4 between the γγ widths of heavy-quark scalar and tensor mesons is significantly modified in the light qq-bar sector. We find however that the helicity-zero amplitude for the γγ coupling of the tensor mesons, which vanishes in the nonrelativistic limit, remains small for light quarks in accord with experimental observation. (author)