Rescattering effects in antiproton-induced exclusive $J/\psi$ and $\psi^\prime$ production on the deuteron

On the basis of the generalized eikonal approximation we study the exclusive reactions $\bar p d \to J/\psi\, n$ and $\bar p d \to \psi^\prime\, n$ in vicinity of the thresholds for charmonium production on a free proton target. It is shown that the rescattering of the incoming antiproton and outgoing charmonium on the spectator neutron leads to a depletion of the charmonium production at low- and to an enhancement at high transverse momenta. This is in qualitative agreement with previous studies of hard proton knockout in proton-deuteron collisions. We analyze different physical sources of uncertainty which may influence the extraction of the total charmonium-neutron cross section. The color transparency effect for the incoming $\bar p$ largely compensates the influence of charmonium rescattering both at low and high transverse momenta. Different choices of the deuteron wave function lead to significant uncertainties at high transverse momenta. As an outcome of the calculations of charmonium production, we also provide predictions on the production of open charm hadrons due to the dissociation of the charmonium on the neutron. It is shown that the open charm production cross section is proportional to the total charmonium-nucleon cross section and quite stable with respect to the variation of other parameters of the model. We thus suggest that open charm channels are most suited for future studies of charmonium-nucleon interactions at PANDA with a deuteron target.