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

Abstract

Theories of the two-photon couplings of $P$-wave positronium and $q\overline{q}$ systems are reviewed and a relationship is found between field-theoretic calculations of $q\overline{q}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and the vector-meson-dominance 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 $\frac{15}{4}$ between the $\ensuremath{\gamma}\ensuremath{\gamma}$ widths of heavy-quark scalar and tensor mesons is significantly modified in the light-$q\overline{q}$ sector. We find however that the helicity-zero amplitude for the $\ensuremath{\gamma}\ensuremath{\gamma}$ coupling of tensor mesons, which vanishes in the nonrelativistic limit, remains small for light quarks, in accord with experimental observation.