Reconciling charmonium production and polarization data in the midrapidity region at hadron colliders within the nonrelativistic QCD framework

A thorough study reveals that the only key parameter for psi (J/psi, psi') polarization at hadron colliders is the ratio < O-psi (S-3(1)[8)>]/< O-psi(P-3(0)[8])> if the velocity scaling rule holds. A slight variation of this parameter results in substantial change of the psi polarization. We find that with equally good description of the yield data, this parameter can vary significantly. Fitting the yield data is therefore incapable of determining this parameter, and consequently, of determining the psi polarization. We provide a universal approach to fixing the long-distance matrix elements (LDMEs) for J/psi and psi' production. Further, with the existing data, we implement this approach, obtain a favorable set of the LDMEs, and manage to reconcile the charmonia production and polarization experiments, except for two sets of CDF data on J/psi polarization.