Abstract
Inclusive production of $\chi_{c J}$ in $e^+e^-$ annihilation is an excellent probe of the role of higher Fock states in the production of heavy quarkonia. Within the non-relativistic QCD approach, contributions from the short-distance production of colour-octet $c\bar{c}$ pairs are significantly larger than those from colour-singlet production. At the same time, $\chi_{c J}$ production rates are significantly smaller than expected in the colour evaporation approach. Measurements of $\chi_{\c J}$ production at CLEO and future B-factories will thus constitute a major test of theoretical approaches to the production of heavy quarkonia.
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