Quarkonium Decay Matrix Elements from Quenched Lattice QCD

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Abstract
The factorization result of Bodwin, Braaten, and Lepage separates the contributions to the decay rates of heavy-quarkonium into long-distance and short-distance factors. The short-distance coefficients are known from perturbation theory. We calculate the long-distance matrix elements for the lowest-lying S- and P-wave states of charmonium and bottomonium in quenched lattice QCD, using a nonrelativistic formulation for the heavy quarks. In particular, we carry out 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.

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