Exploring the two-body strong decay properties of the possible $Λ_cK^{*}$ and $Σ_cK^{(*)}$ molecules

In this work, we apply the effective Lagrangian approach to investigate the two-body strong decay behaviors of the possible $Λ_c K^*$ and $Σ_c K^{(*)}$ molecules, as predicted in our previous study [\href{https://doi.org/10.1103/PhysRevD.108.054011}{Phys. Rev. D \textbf{108}, 054011 (2023)}]. Our results indicate that the decay width for the coupled $Σ_c K / Λ_c K^* / Σ_c K^*$ molecule with $I(J^P) = 1/2(1/2^-)$ is on the order of several MeV, with the $D_s N$ channel being dominant. For the coupled $Λ_c K^* / Σ_c K^*$ molecule with $1/2(1/2^-, 3/2^-)$, the decay widths are on the order of tens of MeV, with the dominant channels being $Σ_c K$ and $Σ_c^* K$, respectively. For the $Σ_c K^*$ molecules with $1/2(1/2^-)$, the decay width can reach one hundred MeV, with $Σ_c K$ and $Λ_c K$ being the dominant decay channels. The decay widths for the $Σ_c K^*$ molecules with $1/2(3/2^-)$ and $3/2(1/2^-)$ are on the order of tens of MeV, with the dominant decay modes being $Σ_c^* K$ and $Σ_c K$, respectively. The branching ratios for all the discussed channels show little dependence on the binding energies.