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Elliptic flow and nuclear modification factors of D-mesons at FAIR in a Hybrid-Langevin approach

The Compressed Baryonic Matter (CBM) experiment at the Facility for Anti-proton and Ion Research (FAIR) will provide new possibilities for charm-quark ($D$-meson) observables in heavy-ion collisions at low collision energies and high baryon densities. To predict the collective flow and nuclear modification factors of charm quarks in this environment, we apply a Langevin approach for the transport of charm quarks in the UrQMD (hydrodynamics + Boltzmann) hybrid model. Due to the inclusion of event-by-event fluctuations and a full (3+1) dimensional hydrodynamical evolution, the UrQMD hybrid approach provides a realistic evolution of the matter produced in heavy-ion collisions. As drag and diffusion coefficients we use a resonance approach for elastic heavy-quark scattering and assume a decoupling temperature of the charm quarks from the hot medium of $130\, \MeV$. Hadronization of the charm quarks to $D$-mesons by coalescence is included. Since the initial charm-quark distribution at FAIR is unknown, we utilize two different initial charm-quark distributions in our approach to estimate the uncertainty of these predictions. We present calculations of the nuclear modification factor, $R_{AA}$, as well as for the elliptic flow, $v_2$, in Pb+Pb collisions at $E_{lab}=25\,\text{AGeV}$. The different medium modifications of $D$-mesons and $\bar{D}$-mesons at high baryon-chemical potential are explored by modified drag- and diffusion-coefficients using the corresponding fugacity factor. Here we find a considerably larger medium modification for $\bar{\mathrm{D}}$- than for $D$-mesons.