Charm hadron production in relativistic heavy ion collisions within a quark combination model

We investigate the charm hadron production in relativistic heavy-ion collisions with the quark combination model. The $p_{T}$ dependencies of the charm baryon to meson ratios such as $\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{0}+\bar{D}^{0}}$, $\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{+}+D^{-}}$ and $\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D_{s}^{+}+D_{s}^{-}}$ in Au+Au collisions at 200 GeV are obtained. The charm baryon enhancement in the intermediate $p_{T}$ range is very prominent, which further, together with the strangeness enhancement, affect the charm hadron ratios and lead to a $\sim17$ larger charm cross-section given by PHENIX. The dependencies of the charm hadron ratios on energy, centrality, and other parameters are also investigated. Predictions of the charm hadron ratios for the upgrade of RHIC and for LHC are presented.