Sequential melting of charmonium states in an expanding Quark Gluon   Plasma and $J/\psi$ suppression at RHIC and LHC energy collisions
  We have developed a hydrodynamic model to study sequential melting of charmonium states in an expanding QGP medium. According to the initial fluid temperature profile, $J/\psi$'s are randomly distributed in the transverse plane. As the fluid evolve in time, the free streaming $J/\psi$'s are suppressed if the local fluid temperature exceed a critical temperature. PHENIX data on the centrality dependence of $J/\psi$ suppression in Au+Au collisions at mid-rapidity are explained by sequential melting of the charmonium states, $\chi_c$, $\psi\prime$ and $J/\psi$, in the expanding medium. The critical temperatures $T_{J/\psi} \approx2.09T_c$ and $T_\chi=T_{\chi_c}=T_{\psi\prime} \approx 1.1T_c$ agree with lattice motivated calculations. The feed-down fraction $F$ depend on whether the cold nuclear matter effect is included or not. It changes from $F=0.3$ with cold nuclear matter effect included to $F=0.5$ when the effect is neglected. Model fails to reproduce the PHENIX data on the centrality dependence of $J/\psi$ suppression in Cu+Cu collisions at mid-rapidity, indicating that the mechanism of $J/\psi$ suppression is different in Au+Au and in Cu+Cu collisions. We also use the model to predict for the centrality dependence of $J/\psi$ suppression in Pb+Pb collisions at LHC energy, $\sqrt{s}$=5500 GeV. In LHC energy, $J/\psi$'s are more suppressed in mid central collisions than in Au+Au collisions at RHIC energy. 
A. K. Chaudhuri