2-PHOTON WIDTH OF SINGLET POSITRONIUM AND QUARKONIUM WITH ARBITRARY TOTAL ANGULAR-MOMENTUM

In this paper we derive GAMMA(gamma-gamma) for S = 0 positronium and quarkonium states with all allowed quantum numbers (J(PC) = 0- +,2- +,4- +, . . .), in both nonrelativistic and relativistic regimes. gamma-gamma-partial widths have previously been published only for fermion-antifermion states with J(PC) = 0+/- +,1+ + (off-shell photons), and 2+/- +. The topic of higher-spin gamma-gamma-partial widths is of current interest in part because a recent nonrelativistic qqBAR calculation for 2- + finds a much smaller gamma-gamma-partial width than the almost-equal-to 1 keV observed for the I = 1, J(PC) = 2- + state pi(2)(1670). We find very large relativistic corrections to the nonrelativistic (contact) approximation for this width as well as large systematic uncertainties in the procedure used to incorporate the physical resonance mass. Our relativistic qqBAR estimate for GAMMA(gamma-gamma)(pi(2)(1670)) is 0.1-0.3 keV, which is somewhat smaller than the experimental value. This discrepancy may only reflect inaccuracies in the theoretical technique. Finally, we quote relativistic numerical results for the gamma-gamma-widths of various 0- +,2- +, and 4- + (uuBAR-ddBAR)/square-root2, ccBAR and bbBAR states in a Coulomb-plus-linear potential model.