Two photon couplings of quarkonium and positronium with general angular quantum numbers

In this dissertation we derive relativistic formulas for the γγ widths of q&qbar; states with general total angular momentum J. Previously, two photon decay widths of q&qbar; states had been calculated relativistically only for states with J^PC = 0^-+, 0⁺⁺ and 2⁺⁺, and very recently these results were supplemented by a nonrelativistic calculation of the l = 2 2^-+ γγ width. This dissertation was suggested by the recent observation of a large γγ width for the I = 2 q&qbar; state π₂(1670), and by the nonrelativistic calculation which predicted a width 2 - 3 orders of magnitude smaller than the measured rate. Motivated by this first observation of a state with l > 1 in γγ collisions, and the numerical inaccuracy of the nonrelativistic prediction for this rate, we derive relativistic quark model results for the Γ_γγ of a general quarkonium state. Our formulas involve a one dimensional overlap integral of the q&qbar; wavefunction in momentum space multiplied by a function of momentum which depends on the quantum numbers of the system. We have confirmed that our formulas reproduce the existing relativistic and nonrelativistic results. We find large relativistic corrections to the absolute rate for light quark systems, and present new numerical results for the Γ_γγ of many interesting q&qbar; systems (q = u, d, s, c, b and t) and helicity selection rules. Finally we apply our nonrelativistic results to positronium, and derive an explicit positronium Γ_γγ for all J^PC in closed form.