Quarkonium Decay Matrix Elements from Quenched Lattice QCD

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Abstract
We calculate the long-distance matrix elements for the decays of the lowest-lying S- and P-wave states of charmonium and bottomonium in quenched lattice QCD, using a nonrelativistic formulation for the heavy quarks. (The short-distance coefficients are known from perturbation theory.) In particular, we present the first calculation from QCD first principles of the color-octet contribution to P-wave decay—a contribution that is absent in potential models. We also give the relations between the lattice matrix elements and their continuum counterparts through one-loop order in perturbation theory.