Muon pair production in radiative decays of heavy quarkonia

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 \(v^2\).

This paper gives results for the spectrum, all allowed E1 radiative partial widths (and some important M1 widths) and all open-charm strong decay amplitudes of all 40 c-cbar states expected up to the mass of the 4S multiplet, just above 4.4 GeV. The spectrum and radiative widths are evaluated using two models, the relativized Godfrey-Isgur model and a nonrelativistic potential model. The electromagnetic transitions are evaluated using Coulomb plus linear plus smeared hyperfine wavefunctions, both in a nonrelativistic potential model and in the Godfrey-Isgur model. The open-flavor strong decay amplitudes are determined assuming harmonic oscillator wavefunctions and the 3P0 decay model. This work is intended to motivate future experimental studies of higher-mass charmonia, and may be useful for the analysis of high-statistics data sets to be accumulated by the BES, CLEO and GSI facilities.