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J/$ψ$ suppression in a dense baryonic medium

We have examined the available latest SPS data on $J/ψ$ suppression in Pb+Pb and In+In collisions at 158 A GeV. Our employed model, with parameters fixed by $p$-$p$ and $p$-nucleus collisions, gives excellent description of NA50 and NA60 data on centrality dependence of $J/ψ$ suppression. The model is then applied to predict the centrality dependence of $J/ψ$ production in Au+Au collisions at FAIR energy domain. A much larger suppression of $J/ψ$ is predicted. In addition the possible effects of a baryon rich medium on $J/ψ$ production is also investigated.