Scanning the Quark-Gluon Plasma with Charmonium

We suggest the variation of charmonium suppression with Feynman x_F in heavy ion collisions as a novel and sensitive probe for the properties of the matter created in such reactions. In contrast to the proton-nucleus case where nuclear suppression is weakest at small x_F, final state interactions with the comoving matter create a minimum at x_F=0, which is especially deep and narrow if a quark-gluon plasma is formed. While a particularly strong effect is predicted at SPS, at the higher RHIC energy it overlaps with the expected sharp variation with x_F of nuclear effects and needs comparison with proton-nucleus data. If thermal enhancement of J/\Psi production takes over at the energies of RHIC and LHC, it will form an easily identified peak, rather than dip in x_F dependence. We predict a steep dependence on centrality and suggest that this new probe is complementary to the dependence on transverse energy, and is more sensitive to a scenario of final state interactions.