J/Ψproduction, $χ$ polarization and Color Fluctuations

The hard contributions to the charmonium- and the bottomium-nucleon cross sections are calculated based on the QCD factorization theorem and the nonrelativistic quarkonium model. We evaluate also the nonperturbative contribution into the charmonium cross sections and show that it dominates these cross sections at $\sqrt{s_{NN}}\approx 20$ GeV (SPS) and becomes a correction at $\sqrt{s_{NN}}\approx 6$ TeV (LHC). The $\J$ production in nucleus-nucleus collisions at the CERN SPS is reasonably well described by hard QCD, when the larger absorption cross sections of the $\chi$ states that are predicted by QCD are taken into account. We predict an $A$-dependent polarization of the $\chi$ states produced in both $pA$ and $AB$ collisions. The expansion of small wave packets is also discussed.