The Photon Spectrum in Quarkonia Decays

Radiative decays of heavy quark bound states have been investigated in the framework of perturbative QCD and have been used to measure the QCD coupling at scales of the order of the heavy quark mass (for recent studies see Refs. [1-3], and references therein). Away from the boundaries of the phase space, the inclusive spectra are expected to be well described by first or second order perturbation theory. Near the phase space boundaries, effects associated with non-perturbative contributions and with high orders in perturbation theory are expected to become important. In this paper I focus on two of these effects. First, I describe the role of the fragmentation of gluons and light quarks into a photon. This is relevant to the shape of the inclusive photon spectrum at small z, where z = 2Eγ/M is the energy fraction carried by the photon, with M being the quarkonium mass. Second, I consider the opposite end of the spectrum, z → 1. I discuss the resummation of soft gluons in this region and its physical implications. Consider the decay of a S1 quarkonium state into a prompt photon plus hadrons: XQQ̄ → γ + hadrons . (1)