Current Issues in Quarkonium Production

As a stringent test of the nonrelativistic QCD factorization approach for inclusive heavy-quarkonium production in high-energy hadron collision, the polarized heavyquarkonium production at the Tevatron is discussed. The polarization of prompt J/ψ at the Tevatron is predicted within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The prediction agrees with measurements from the CDF collaboration at intermediate values of pT , but disagrees at the large values of pT measured. Recent preliminary data of heavy quarkonia from CDF and theoretical/experimental prospects related to the Run II heavy quarkonium physics are also discussed.