The masses and decay widths of the S-wave ΛcΛ̄c bound states

In this work, we investigate possible bound states of the ΛcΛ̄c system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation, we confirm the existence of ΛcΛ̄c bound states with quantum numbers JPC=0⁻⁺ and JPC=1⁻⁻. We further investigate the partial decay widths of the ΛcΛ̄c bound states into NN̄, DD̄, DD̄^, D^̄^, ππ̄, and KK̄. Our results indicate that the decay width of the ΛcΛ̄c bound state with JPC=1⁻⁻ is much larger than that with JPC=0⁻⁺, and among their decay channels, the DD̄^ final state is the main decay mode. We suggest experiments to search for the ΛcΛ̄c bound states in the DD̄^ final state.