Energy dependence of $J/\psi$ absorption in proton-nucleus collisions

Charmonium states are expected to be considerably suppressed in the case of quark-gluon plasma formation in high-energy heavy-ion collisions. However, a robust identification of suppression patterns as signatures of a deconfined QCD medium requires a detailed understanding of the "normal nuclear absorption" already present in proton-nucleus collisions, where the charmonium production cross sections increase less than linearly with the number of target nucleons. We analyse the J/$\psi$ production cross sections measured in proton-nucleus collisions in fixed target experiments, with proton beam energies from 200 to 920~GeV, and in d-Au collisions at RHIC, at $\sqrt{s_{_{NN}}}=200$~GeV, in the framework of the Glauber formalism, using several sets of parton distributions with and without nuclear modifications. The results reveal a significant dependence of the "absorption cross section" on the kinematics of the J/$\psi$ and on the collision energy. Extrapolating the observed patterns we derive the level of absorption expected at $E_{\rm lab} = 158$~GeV, the energy at which the heavy-ion data sets were collected at the CERN SPS.