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We build up a model to reproduce the experimentally measured $R_{AA}$ of$J/\psi$ near midrapidty in Au+Au collision at $\sqrt{s_{NN}}=200$ GeV. Themodel takes into account the $J/\psi$ suppression from the quark-gluon plasmaand hadron gas as well as the nuclear absorption of primordial charmonia andthe regeneration effects at the hadronization stage, and hence is ageneralization of the two component model introduced by Grandchamp and Rapp.The improvements in this work are twofold; the addition of the initial localtemperature profile and a consistent use of QCD NLO formula for both thedissociation cross section in the hadron gas and the thermal decay widths inthe quark-gluon plasma for the charmonium states. The initial local temperatureprofile is determined from the assumption that the local entropy density isproportional to a formula involving the number densities of the number ofparticipants and of the binary collisions that reproduces the multiplicities ofcharged particles at chemical freeze-out. The initial local temperature profilebrings about a kink in the $R_{AA}$ curve due to the initial melting of$J/\psi$. The initially formed fireball, composed of weakly interacting quarksand gluons with thermal masses that are extracted from lattice QCD, follows anisentropic expansion with cylindrical symmetry. The fit reproduces well theAu+Au as well as the Cu+Cu data. The same method is applied to predict the$R_{AA}$ expected from the Pb+Pb collision at LHC energy.

$R_{AA}$ of $J/\psi$ near mid-rapidity in heavy ion collisions at $\sqrt{s_{NN}}=200$ GeV