Charmonium and open charm production in nuclear collisions at SPS/FAIR energies and the possible influence of a hot hadronic medium

We provide predictions for charmonium and open charm production in nuclear collisions at SPS/FAIR energies within the framework of the statistical hadronization model. The increasing importance at lower energies of Lambda_c production is demonstrated and provides a challenge for future experiments. We also demonstrate that, because of the large charm quark mass and the different timescales for charm quark and charmed hadron production, possible modifications of charmed hadrons in the hot hadronic medium do not lead to measurable changes in cross sections for D-meson production. A possible influence of medium effects can be seen, however, in yields of charmonium. These effects are visible at all energies and results are presented for the energy range between charm threshold and RHIC energy.