## Quarkonium Decay Matrix Elements from Quenched Lattice QCD

We calculate the long-distance matrix elements for the decays of the lowest-lying {ital S}- and {ital 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 {ital P}-wave decay{emdash}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. {copyright} {ital 1996 The American Physical Society.}