Mev, corresponding to $ T/T_c \sim 1.9 $ while for the $3 S$ states the total melting happens at $ T \sim 220 $ MeV, that means $T/T_c \sim  1.2  $.

Then figure [**3** ]{} shows the spectral functions for the charmonium vector states at four different temperatures that illustrate the melting process. More details for the thermal evolution of charmonium states are shown in appendix [**A**]{} . One can clearly see the change from the case with three well defined peaks corresponding to the states $1S, 2S$ and $3S$ to the case where there is no well defined quasi particle state. An important difference with respect to the bottomonium case is that the melting process occurs at temperatures below $T_c$. At the critical temperature there is only a very small peak of the state $1S$, so one can interpret this situation as meaning that the charmonium states $ 2S$ and $3S$ do not survive in the deconfined plasma phase, while there could be some trace of the $1 S$ state up to temperatures of $ 1.2 T_c$.

The present results for bottomonium states are consistent with the ones obtained using lattice QCD in [@Suzuki:2012ze]. This article predicts a lower 