Sum rules for radiative quarkonium decays from short-range interactions

Sum rules previously derived for proton decay are extended and applied to treat effects of bound states spectroscopy on radiative quarkonium decays. The transition involves boson (photon or pion) emission followed by quark annihilation. Sum rules for the contributions from different intermediate bound states are derived by using closure and the assumptions (1) that the boson emission is described by a plane wave or multipole operator which satisfies a wave equation, and (2) that the annihilation depends on the bound state wave function or its derivative at the origin.