Kinematic effects in radiative quarkonia decays

Abstract

Nonrelativistic QCD (NRQCD) predicts color octet contributions to be significant not only in many production processes of heavy quarkonia but also in their radiative decays. We investigate the photon energy distributions in these processes in the end point region. There the velocity expansion of NRQCD breaks down which requires a resummation of an infinite class of color octet operators to so-called shape functions. We model these nonperturbative functions by the emission of a soft gluon cluster in the initial state. We found that the spectrum in the end point region is poorly understood if the values for the color octet matrix elements are taken as large as indicated from NRQCD scaling rules. Therefore the end point region should not be taken into account for a fit of the strong coupling constant at the scale of the heavy quark mass.