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D mesons and charmonium states in asymmetric nuclear matter at finite temperatures

We investigate the in-medium masses of $D$ and $\bar{D}$ mesons in the isospin-asymmetric nuclear matter at finite temperatures arising due to the interactions with the nucleons, the scalar isoscalar meson $σ$, and the scalar iso-vector meson $δ$ within a SU(4) model. The in-medium masses of $J/ψ$ and the excited charmonium states ($ψ(3686)$ and $ψ(3770)$) are also calculated in the hot isospin asymmetric nuclear matter in the present investigation. These mass modifications arise due to the interaction of the charmonium states with the gluon condensates of QCD, simulated by a scalar dilaton field introduced to incorporate the broken scale invariance of QCD within the effective chiral model. The change in the mass of $J/ψ$ in the nuclear matter with the density is seen to be rather small, as has been shown in the literature by using various approaches, whereas, the masses of the excited states of charmonium ($ψ(3686)$ and $ψ(3770)$) are seen to have considerable drop at high densities. The present study of the in-medium masses of $D$ ($\bar{D}$) mesons as well as of the charmonium states will be of relevance for the observables from the compressed baryonic matter, like the production and collective flow of the $D$ ($\bar D$) mesons, resulting from the asymmetric heavy ion collision experiments planned at the future facility of the FAIR, GSI. The mass modifications of $D$ and $\bar{D}$ mesons as well as of the charmonium states in hot nuclear medium can modify the decay of the charmonium states ($Ψ^{'}, χ_{c}, J/Ψ$) to $D\bar{D}$ pairs in the hot dense hadronic matter. The small attractive potentials observed for the $\bar{D}$ mesons may lead to formation of the $\bar{D}$ mesic nuclei.