$J/\psi$ suppression in the threshold model at RHIC and LHC energy

In the QGP based threshold model \cite{Blaizot:2000ev,Blaizot:1996nq}, in addition to the normal nuclear absorption, $J/\psi$'s are subjected to an 'anomalous' suppression such that above a threshold density $n_{J/\psi}$, all the $J/\psi$'s are melted. In the threshold model we have analysed the recent PHENIX data on the centrality dependence of $J/\psi$ suppression in Au+Au collisions at RHIC. Feedback from decay of the state $\chi$ is accounted for. $J/\psi$'s are anomalously suppressed above a threshold density, $n_{J/\psi}=3.57\pm 0.17$ $fm^{-2}$. Threshold density for anomalous suppression of the state $\chi$ is uncertain to a large extent, $n_\chi=0.32 \pm 0.32$ $fm^{-2}$. The fraction $F$ of the state $\chi$ can not be determined unambiguously, depending on the nuclear absorption, it can vary from 20% to 40%. We have also predicted for the suppression in Pb+Pb collisions at LHC energy. In central Pb+Pb collisions, $J/\psi$'s are suppressed by a factor of 3-4. Suppression pattern is rather similar to that in Au+Au collisions, if not slighty less in central collisions. Using the PHENIX data on the participant number dependence of the Bjorken energy density, we have also estimated the QGP formation time. For critical temperature $T_c$=192 MeV, estimated QGP formation time ranges between 0.07-0.09 fm/c.