Quarkonium production: velocity-scaling rules and long-distance matrix elements

The hierarchy of long-distance matrix elements (MEs) for quarkonium production depends on their scaling with the velocity $v$ of the heavy quark in the bound state. Ranges for the velocities in various bound states and uncertainties of colour-singlet MEs are estimated in a quark-potential model. Different possibilities for the scaling with $v$ of the MEs are discussed; they depend on the actual values of $v$ and the QCD scale. As an application, J/psi polarization in e^+e^- annihilation is discussed. The first non-perturbative estimates of colour-octet MEs are presented and compared with phenomenological determinations. Finally, various predictions of prompt quarkonium production at LEP are compared.