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Open charm meson in nuclear matter at finite temperature beyond the zero range approximation

The properties of open charm mesons, $D$, $\bar D$, $D_s$ and $\bar D_s$ in nuclear matter at finite temperature are studied within a self-consistent coupled-channel approach. The interaction of the low lying pseudoscalar mesons with the ground state baryons in the charm sector is derived from a $t$-channel vector-exchange model. The in-medium scattering amplitudes are obtained by solving the Lippmann-Schwinger equation at finite temperature including Pauli blocking effects, as well as $D$, $\bar D$, $D_s$ and $\bar D_s$ self-energies taking their mutual influence into account. We find that the in-medium properties of the $D$ meson are affected by the $D_s$-meson self-energy through the intermediate $D_s Y$ loops coupled to $DN$ states. Similarly, dressing the $\bar{D}$ meson in the $\bar{D}Y$ loops has an influence over the properties of the $\bar{D}_s$ meson.