Open charm and charmonium production at relativistic energies

We calculate open charm and charmonium production in $Au+Au$ reactions at $\sqrt{s}$ = 200 GeV within the hadron-string dynamics (HSD) transport approach employing open charm cross sections from $pN$ and $\pi N$ reactions that are fitted to results from PYTHIA and scaled in magnitude to the available experimental data. Charmonium dissociation with nucleons and formed mesons to open charm ($D+\bar{D}$ pairs) is included dynamically. The 'comover' dissociation cross sections are described by a simple phase-space model including a single free parameter, i.e. an interaction strength $M_0^2$, that is fitted to the $J/\Psi$ suppression data for $Pb+Pb$ collisions at SPS energies. As a novel feature we implement the backward channels for charmonium reproduction by $D \bar{D}$ channels employing detailed balance. From our dynamical calculations we find that the charmonium recreation is comparable to the dissociation by 'comoving' mesons. This leads to the final result that the total $J/\Psi$ suppression at $\sqrt{s}$ = 200 GeV as a function of centrality is slightly less than the suppression seen at SPS energies by the NA50 Collaboration, where the 'comover' dissociation is substantial and the backward channels play no role. Furthermore, even in case that all directly produced $J/\Psi$ mesons dissociate immediately (or are not formed as a mesonic state), a sizeable amount of charmonia is found asymptotically due to the $D+\bar{D} \to J/\Psi$ + meson channels in central collisions of $Au+Au$ at $\sqrt{s}$ = 200 GeV which, however, is lower than the $J/\Psi$ yield expected from binary scaling of $pp$ collisions.