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Recent data from the Tevatron collider have revealed that the production
rate of prompt charmonium at large transverse momentum is orders of magnitude
larger than the best theories of a few years ago had predicted. These
surprising results can be understood by taking into account two recent
developments that have dramatically revised the theoretical description of
heavy-quarkonium production. The first is the realization that fragmentation
must dominate at large transverse momentum, which implies that most charmonium
in this kinematic region is produced by the hadronization of individual
high-pT partons. The second is the development of a
factorization formalism for quarkonium production based on nonrelativistic QCD
that allows the formation of charmonium from color-octet
pairs to be treated systematically. This review summarizes these theoretical
developments and their implications for quarkonium production in high-energy
colliders.
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