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Abstract
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 4-fermion operators in nonrelativistic QCD, with coefficients that can be computed
using perturbation theory in the coupling constant \(\alpha_s(M)\). 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, up to corrections of relative order
\(v^3\), and of P-wave states, up to corrections of relative order \(v^2\).
Comments Revised to clarify the velocity-scaling rules for spin-flip
transitions, to correct error estimates, and to emphasize probabilities of
Fock states, rather than amplitudes, 117 pages in REVTEX plus 11 Postscript
figures. Erratum to Phys. Rev. D article included as a separate file, 4 pages
in REVTEX