Spectral functions for $\bar{D}$ meson and $\bar{D}_0^*$ meson in nuclear matter with partial restoration of chiral symmetry

We investigate the in-medium masses of a $\bar{D} (0^-)$ meson and a $\bar{D}_0^* (0^+)$ meson and spectral functions for $\bar{D}$ and $\bar{D}_0^*$ meson channels in nuclear matter. These mesons are introduced as chiral partner in the chiral symmetry broken vacuum, hence they are useful to explore the partial restoration of the broken chiral symmetry in nuclear matter. We consider the linear sigma model to describe the chiral symmetry breaking. Our study shows that the loop corrections to $\bar{D}$ and $\bar{D}_0^*$ meson masses provide a smaller mass splitting at finite density than that in vacuum, whose result indicates a tendency of the restoration of the chiral symmetry. We investigate also the spectral function for $\bar{D}_0^*$ meson channel, and find three peaks. The first peak which corresponds to the resonance of $\bar{D}_0^*$ meson is broadened by collisions with nucleons in medium, and the peak position shifts to lower mass due to the partial restoration of chiral symmetry as the density increases. The second peak is identified as a threshold enhancement which shows a remarkable enhancement as the density increase. The third peak is Landau damping. The obtained properties of $\bar{D}$ and $\bar{D}_0^*$ mesons in nuclear matter will provide useful information for experiments.