Novel approach to decays, gluon distributions, and fragmentation functions of heavy quarkonia

An effective, low-energy, field theory of s-wave quarkonia, constituent heavy quarks, and gluons is constructed which is manifestly gauge invariant. The interaction Lagrangian has the form of a twist expansion, as typically encountered in hard processes, and involves derivatives of arbitrary order. The parameters in the interaction are related with the nonrelativistic wave function, and standard results for QQ¯ inclusive decays and radiative transitions are shown to be easily recovered. The light-cone gluon momentum distribution at very small x is calculated and shown to be uniquely determined by the nonrelativistic wave function. The distribution has a part which goes as ${\mathit{x}}^{\mathrm{-}1}$ ln x, i.e., is more singular than the usually assumed 1/x behavior. The fragmentation function for a virtual gluon to inclusively decay into an ${\mathrm{\eta }}_{\mathit{c}}$ or ${\mathrm{\eta }}_{\mathit{b}}$ is also calculated. We find that the emission of low momentum gluons makes this process quite sensitive to assumptions about the binding energy of heavy quarks in quarkonia.