Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium

A rigorous QCD analysis of the inclusive annihilation decay rates of heavy quarkonium states is presented. The effective-field-theory framework of nonrelativistic QCD is used to separate the short-distance scale of annihilation, which is set by the heavy quark mass M, from the longer-distance scales associated with quarkonium structure. The annihilation decay rates are expressed in terms of nonperturbative matrix elements of four-fermion operators in nonrelativistic QCD, with coefficients that can be computed using perturbation theory in the coupling constant ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(M). The matrix elements are organized into a hierarchy according to their scaling with v, the typical velocity of the heavy quark. An analogous factorization formalism is developed for the production cross sections of heavy quarkonium in processes involving momentum transfers of order M or larger. The factorization formulas are applied to the annihilation decay rates and production cross sections of S-wave states at next-to-leading order in ${\mathit{v}}^{2}$ and P-wave states at leading order in ${\mathit{v}}^{2}$.