Relativistic formulation of the radiative transition of charmonium and b-quarkonium

In this work we develop a relativistic formalism for calculating the radiative transition rates of a fermion-antifermion bound state. We calculate the radiative decay rates in charmonium and b-quarkonium systems and find them generally in better agreement with experiment than other previous works, in particular for the case of hindered magnetic transition of ψ'. Our relativistic formalism automatically includes the effect of the recoil of the final bound state or, equivalently, a sum over all multipoles, which is important in mesonic radiative transitions. It also treats both quark and antiquark as four component spinors to given relativistic currents, and includes a natural mixing of L-S terms for a given J and parity. We discover the importance of systematic inclusion of these relativistic effects by comparing our relativistic results with a nonrelativistic calculation. The quark-antiquark interaction at short distances has the form of an asymptotic free vector gluon exchange and its only parameter is αQCD or the effective ΛR for the bound state. At large distances the interaction is an effective scalar exchange which is the linear confining potential, and its slope is found by the fit to the charmonium levels. In the nonrelativisitc limit the interactions reduce to the Richardson potential. This bound state formalism was previously used to calculate the masses and leptonic decay widths of mesons composed of both light and heavy quarks