Production of heavy quarkonium in high energy colliders

Recent data from the Tevatron has revealed that the production rate of prompt charmonium at large transverse momentum is orders of magnitude larger than the best theoretical predictions of a few years ago. These surprising results can be understood by taking into account two recent developments that have revolutionized 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-p_T 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 c \bar c pairs to be treated systematically. This review summarizes these theoretical developments and their implications for quarkonium production in high energy colliders