Relativistic corrections to dipole decay amplitudes in quarkonium

Abstract

We study the leading relativistic correction to the dipole amplitude for a radiative transition between bound states of two spin-½ particles with arbitrary anomalous magnetic moments and masses. For the part of the correction which corresponds to a modification of the dipole operator, and which is spin-dependent, our results reduce, in the equal-mass case, to those given by earlier authors. There is another part, which arises from perturbing the initial and final wave functions with the fine-structure operator. We give the results of a numerical calculation which indicates that in the case of charmonium the wave-function effect can be larger than that arising from the dipole-operator modification.