Rapidity Dependence of $J/\psi$ Production at RHIC and LHC

The motion of charmonium in heavy ion collisions is described by a three dimensional transport equation with initial production and continuous regeneration in hot medium. The observation of apparently stronger $J/\psi$ suppression at forward rapidity compared to that at midrapidity, so called $J/\psi$ puzzle at RHIC, can well be explained by the competition between the two production mechanisms. At LHC, however, the rapidity dependence of the $J/\psi$ production is dominated by the regeneration process.