Quarkonium Production and Proposal of the New Experiments on Fixed Target at the LHC

The brief review of the experimental data on quarkonium productions measured at the CERN SPS, at the Brookhaven Collider RHIC, and at the LHC is presented. The dissociation of quarkonium resonances produced in heavy ion collisions was suggested as a possible signal of the Quark-Gluon Plasma formation. At the CERN SPS, the anomalous suppression of the J/ψ production was observed in central Pb-Pb collisions by the NA50 collaboration. However, the effects of J/ψ suppression on cold nuclear matter, feed-down production from higher charmonium states, and regeneration processes should be taken into account. If proton and ion beams at the LHC will be used with fixed targets, the energy interval between the SPS energy and the nominal RHIC energy (200 GeV) could be investigated. The high statistics data on quarkonium productions at these energies will give the possibility of clarifying the mechanism of charmonium productions to investigate the importance of the recombination process, since the probability of recombination decreases with decreasing the energy of collisions.