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Probing the interactions of charmed mesons with nuclei in $\bar p$ induced reactions

We study the perspectives of resonant and nonresonant charmed meson production in $\bar{p} + A$ reactions within the Multiple Scattering Monte Carlo (MSMC) approach. We calculate the production of the resonances $Ψ(3770), Ψ(4040)$ and $Ψ(4160)$ on various nuclei, their propagation and decay to $D, \bar{D}, D^*, \bar{D}^*, D_s, \bar{D}_s$ in the medium and vacuum, respectively. The modifications of the open charm vector mesons in the nuclear medium are found to be rather moderate or even small such that dilepton spectroscopy will require an invariant mass resolution of a few MeV. Furthermore, the elastic and inelastic interactions of the open charm mesons in the medium are taken into account, which can be related to $(u,d)$-, $s$- or $c$-quark exchange with nucleons. It is found that by studying the $D/\bar{D}$ ratio for low momenta in the laboratory ($\leq 2-2.2$ GeV/c) as a function of target mass $A$ stringent constraints on the $c$-quark exchange cross section can be obtained. On the other hand, the ratios $D^-_s/D^+_s$ as well as $D/D^-_s$ and $D/D^+_s$ at low momenta as a function of $A$ will permit to fix independently the strength of the $s$-quark exchange reaction in $D^-_s N$ scattering.