Charmed Hadrons from Coalescence plus Fragmentation in relativistic nucleus-nucleus collisions at RHIC and LHC

In a coalescence plus fragmentation approach we calculate the heavy baryon/meson ratio and the $p_T$ spectra of charmed hadrons $D^{0}$, $D_{s}$ and $\Lambda_{c}^{+}$ in a wide range of transverse momentum from low $p_T$ up to about 10 GeV and discuss their ratios from RHIC to LHC energies without any change of the coalescence parameters. We have included the contribution from decays of heavy hadron resonances and also the one due to fragmentation of heavy quarks which do not undergo the coalescence process. The coalescence process is tuned to have all charm quarks hadronizing in the $p_T\rightarrow 0$ limit and at finite $p_T$ charm quarks not undergoing coalescence are hadronized by independent fragmentation. The $p_T$ dependence of the baryon/meson ratios are found to be sensitive to the masses of coalescing quarks, in particular the $\Lambda_{c}/D^{0}$ can reach values of about $\rm 1\div 1.5 $ at $p_T \approx \, 3$ \mbox{GeV}, or larger, similarly to the light baryon/meson ratio like $p/\pi$ and $\Lambda/K$, however a marked difference is a quite weak $p_T$ dependence with respect to the light case, such that a larger value at intermediate $p_T$ implies a relatively large value also for the integrated yields. A comparison with other coalescence model and with the prediction of thermal model is discussed.