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Parton shadowing and $J/ψ$-to-Drell-Yan ratio in nuclear collisions at SPS and FAIR

We have analyzed the data on $J/ψ$-to-Drell-Yan production cross section ratio in proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions, measured by the NA50 collaboration in the SPS energy domain. Two component QVZ model has been employed to calculate $J/ψ$ production cross sections. For both $J/ψ$ and Drell-Yan production, nuclear modifications to the free nucleon structure functions are taken into account. In heavy-ion collisions, such modifications are assumed to be proportional to the local nuclear density resulting in centrality dependent initial state effects. Differences in quark and gluon shadowing leads to a new source of impact parameter dependence of the $J/ψ$ to Drell-Yan production ratio. For $J/ψ$, final state interaction of the produced $c\bar{c}$ pairs with the nuclear medium is also taken into account. A satisfactory description of the data in both $p+A$ and $A+A$ collisions is obtained. Role of the shadowing corrections are investigated in detail. Model calculations are extrapolated to predict the centrality dependence of $J/ψ$-to-Drell-Yan ratio in the FAIR energy regime.