Charmonium production in heavy-ion collisions from SPS to LHC

Using the two-component model that includes charmonium production from initial nucleon-nucleon hard scattering and regeneration in the produced quark-gluon plasma, we study $J/\psi$ production in heavy ion collisions at SPS, RHIC and LHC. For the expansion dynamics of produced hot dense matter, we use a schematic viscous hydrodynamic model with the specific shear viscosity taken, respectively, to be twice and ten times the lower bound of $1/4\pi$ suggested by the Ads/CFT correspondence in the quark-gluon plasma and in the hadron gas. For the initial dissociation and the subsequent thermal decay of charmonia in the hot dense matter, we use the screened Cornell potential to describe the properties of charmonia and the perturbative QCD to calculate their dissociation cross sections. Including regeneration of charmonia in the quark-gluon plasma via a kinetic equation with in-medium chamonium decay widths, we obtain a good description of measured nuclear modification factors at SPS and RHIC. A reasonable description of measured nuclear modification factor of $J/\psi$s of high transverse momenta in heavy ion collisions at LHC is also obtained if we include the contribution to the $J/\psi$ yield from the decay of bottomed hadrons.