Relativistic formulation of the radiative transitions of charmonium and b-quarkonium.

Bander, Silverman, Klima, and Maor recently developed a relativistic formalism for quark-antiquark bound states. It was used to calculate the spectra and leptonic decay widths of charmonium, b-quarkonium, D mesons, F mesons, B mesons, and mesons composed of light quarks. The form of the interactions between quark and antiquark was highly motivated by QCD. We extend this relativistic treatment to a relativistic formulation of radiative decays that automatically takes into account the effects of recoil, uses boosted final-state meson wave functions, includes relativistic bound-state wave functions involving relativistic mixtures of terms, and treats the valence quarks as four-component spinors. We then calculate radiative transition rates of the charmonium and b-quarkonium systems in this formalism and find that transitions which can be compared with experiment are in good agreement. Predictions are also made for decays that are not yet measured. © 1987 The American Physical Society