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

Abstract

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, ${}_{\bar{\mathrm{D}}}^{40}\mathrm{Ca}$ and ${}_{\bar{\mathrm{D}}}^{208}\mathrm{Pb}$, 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.

Comments: 21 pages, 9 figures