Detailed Rapidity Dependence of $J/\psi$ Production at LHC

$J/\psi$ suppression with rapidity is studied with both (3+1) dimensional transport equation and hydrodynamics in details at $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. In central rapidity region of the hot medium, $J/\psi$ nuclear modification factor shows weak rapidity dependence due to the boost invariance of the medium. But in forward rapidity region for entire transverse momentum bin, $J/\psi$ regeneration is strongly suppressed due to the decreasing charm pair cross section. This makes $J/\psi$ $R_{AA}(y)$ decrease with rapidity. The ratio $r_{AA}$ of mean transverse momentum square in AA collisions to that in pp collisions increases strongly in forward rapidity region and is more sensitive to the $J/\psi$ production mechanisms.