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The dominant production mechanism for heavy-quark--antiquark bound states with large transverse momentum is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions D (z, ) describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant.
Braaten et al. (Mon,) studied this question.