Two Gamma Quarkonium and Positronium Decays with Two-Body Dirac Equations of Constraint Dynamics

Abstract

Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schrodinger equation. Unlike other three-dimensional truncations of the Bethe-Salpeter equation, this covariant formalism has been thoroughly tested in nonperturbatives contexts in QED, QCD, and nucleonnucleon scattering. Here we continue the important studies of this formalism by extending a method developed earlier for positronium decay into two photons to tests on the sixteen component quarkonium wave function solutions obtained in meson spectroscopy. We examine positronium decay and then the two-gamma quarkonium decays of ηc, η′c, χc0, χc2, and π0. The results for the π0, although off the experimental rate by 13%, is much closer than the usual expectations from a potential model.