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

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