The masses and decay widths of the $S$-wave ${\Lambda }_c{\bar{\Lambda }}_c$ bound states

Abstract

In this work, we investigate possible bound states of the ${\Lambda }_c{\bar{\Lambda }}_c$ system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation, we confirm the existence of ${\Lambda }_c{\bar{\Lambda }}_c$ bound states with quantum numbers $J^{PC}=0^{-+}$ and $J^{PC}=1^{--}$. We further investigate the partial decay widths of the ${\Lambda }_c{\bar{\Lambda }}_c$ bound states into $N\bar{N}$, $D\bar{D}$, $D{\bar{D}}^{\ast }$, $D^{\ast }{\bar{D}}^{\ast }$, $\pi \bar{\pi }$, and $K\bar{K}$. Our results indicate that the decay width of the ${\Lambda }_c{\bar{\Lambda }}_c$ bound state with $J^{PC}=1^{--}$ is much larger than that with $J^{PC}=0^{-+}$, and among their decay channels, the $D{\bar{D}}^{\ast }$ final state is the main decay mode. We suggest experiments to search for the ${\Lambda }_c{\bar{\Lambda }}_c$ bound states in the $D{\bar{D}}^{\ast }$ final state.