Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium

Details Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium

1994-07-20

arxiv.org/abs/hep-ph/9407339v2

Phys.Rev. D51 (1995) 1125-1171; Erratum-ibid. D55 (1997) 5853

Physics

High Energy Physics

High Energy Physics - Phenomenology

Revised to clarify the velocity-scaling rules for spin-flip transitions, to correct error estimates, and to emphasize probabil

Scientific paper

10.1103/PhysRevD.51.1125

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 $v^2$.

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