Novel approach to decays, gluon distributions, and fragmentation functions of heavy qurakonia
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 non-relativistic wave function, and standard results for $Q\bar{Q}$ 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 non-relativistic wave function. The distribution has a part which goes as $x^{-1}logx$, ie. is more singular than the usually assumed $1/x$ behaviour. The fragmentation function for a virtual gluon to inclusively decay into an $η_c$ or $η_b$ is also calculated. We find that the emission of low momentum gluons makes this process quite sensitive to assumptions about the binding of heavy quarks in quarkonia.