We study the properties of open-charm mesons (D and (D) over bar) in nuclear matter at finite temperature within a self-consistent coupled-channel approach. The meson-baryon interactions are adopted from a type of broken SU(4) s-wave Tomozawa-Weinberg term supplemented by an attractive scalar-isoscalar interaction. The in-medium solution at finite temperature incorporates Pauli blocking effects, mean-field binding on all the baryons involved, and pi and open-charm meson self-energies in a self-consistent manner. In the DN sector, the Lambda(c) and Sigma(c) resonances, generated dynamically at 2593 and 2770 MeV in free space, remain close to their free-space position while acquiring a remarkable width due to the thermal smearing of Pauli blocking as well as from the nuclear matter density effects. As a result, the D meson spectral density shows a single pronounced peak for energies close to the D meson free-space mass that broadens with increasing matter density with an extended tail particularly toward lower energies. The (D) over bar potential shows a moderate repulsive behavior coming from the dominant I=1 contribution of the (D) over barN interaction. The low-density theorem is, however, not a good approximation for the (D) over bar self-energy in spite of the absence of resonance-hole contributions close to threshold in this case. We speculate the possibility of D-mesic nuclei as well as discuss some consequences for the J/Psi suppression in heavy-ion collisions, in particular for the future CBM experiment at FAIR.
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