The masses and decay widths of the $S$-wave $Λ_c\barΛ_c$ 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 $J<sup>{PC}=0<sup>{-+}$ and $J<sup>{PC}=1<sup>{--}$. We further investigate the partial decay widths of the $\Lambda_c\bar{\Lambda}_c$ bound states into $N\bar{N}$, $D\bar{D}$, $D\bar{D}<sup>\ast$, $D<sup>\ast\bar{D}<sup>\ast$, $\pi\bar{\pi}$, and $K\bar{K}$. Our results indicate that the decay width of the $\Lambda_c\bar{\Lambda}_c$ bound state with $J<sup>{PC}=1<sup>{--}$ is much larger than that with $J<sup>{PC}=0<sup>{-+}$, and among their decay channels, the $D\bar{D}<sup>\ast$ final state is the main decay mode. We suggest experiments to search for the $\Lambda_c\bar{\Lambda}_c$ bound states in the $D\bar{D}<sup>\ast$ final state.