The Octet Structure Function and Radiative Quarkonia Decay

The Operator Product Expansion, in conjunction with the power counting of non-relativistic field theory, is used to examine the end-point region of the radiative decay of heavy quark bound states with $^3S_1$ quantum numbers, $Q\bar{Q} \to \gamma+X$. We identify an infinite class of operators that determine the shape of the photonic end-point spectrum. These operators can be resummed to form an octet structure function which parameterizes the energy of the dynamical gluon content of the leading octet Fock state component of the quarkonium. This color octet contribution is important when the photon spectrum is examined with a resolution given by$\Delta E_\gamma \sim m_Qv^2$, where $v^2$ is the relative quark velocity squared. The formalism used makes explicit the shift of the end-point from its partonic to its hadronic value.