$\bar{\mathrm{D}}$ and $\mathrm{B}$ mesons in nuclear medium

We discuss the mass modifications of $\bar{\mathrm{D}}$ and $\bar{\mathrm{D}}^{\ast}$ ($\mathrm{B}$ and $\mathrm{B}^{\ast}$) mesons in nuclear medium. The heavy quark symmetry for $\bar{\mathrm{D}}$ and $\bar{\mathrm{D}}^{\ast}$ ($\mathrm{B}$ and $\mathrm{B}^{\ast}$) mesons is adopted, and the interaction between a $\bar{\mathrm{D}}$ or $\bar{\mathrm{D}}^{\ast}$ ($\mathrm{B}$ or $\mathrm{B}^{\ast}$) meson and a nucleon is supplied from the pion exchange. We find the negative mass shifts for $\bar{\mathrm{D}}$ meson and $\mathrm{B}$ meson, and hence that the $\bar{\mathrm{D}}$ and $\mathrm{B}$ mesons are bound in the nuclear medium. As applications, we consider the atomic nuclei with a $\bar{\mathrm{D}}$ meson, $^{40}_{\bar{\mathrm{D}}}\mathrm{Ca}$ and $^{208}_{\bar{\mathrm{D}}}\mathrm{Pb}$, and investigate the energy levels of the $\bar{\mathrm{D}}$ meson in each nucleus. We also discuss the mass shifts in the isospin asymmetric nuclear medium, and present the possible phenomenon about distribution of isospin density around a $\bar{\mathrm{D}}$ or $\mathrm{B}$ meson in nuclear medium. We find that the mass shifts of $\bar{\mathrm{D}}^{\ast}$ and $\mathrm{B}^{\ast}$ mesons have large imaginary parts, which would prevent precise study of the energy levels of $\bar{\mathrm{D}}^{\ast}$ and $\mathrm{B}^{\ast}$ mesons in nuclei.