Inclusive decays of heavy quarkonium to light particles

We derive the imaginary part of the potential nonrelativistic QCD (pNRQCD) Hamiltonian up to order (Formula presented) when the typical momentum transfer between the heavy quarks is of the order of (Formula presented) or greater, and the binding energy E much smaller than (Formula presented) We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to (Formula presented) and (Formula presented) times a short-distance coefficient, for (Formula presented) and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown nonperturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal nonperturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal nonperturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.