Strong decays of the $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ in the $ND^{*}$ molecular frame

Stimulated by the observation of a new structure, named $\Lambda_{c}(2910)$, in the $\Sigma_{c}(2455)^{0,++}\pi^{+,-}$ decay channel from B meson decay process by the Belle Collaboration, and the similarity of the $\Lambda_{c}(2910)/\Lambda_{c}(2940)$ and $P_{c}$ states, we investigate the decay behavior of the $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ in the $N D^{*}$ molecular frame with the possible $J^{P}$ quantum numbers to be $1/2^{-}$ and $3/2^{-}$. We employ an effective Lagrangian approach to evaluate the partial widths of $ND$, $\Sigma_{c}\pi$ and $\Sigma_{c}^{*}\pi$ channels. The estimations in the present work indicate that the $J^P$ quantum numbers of $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ are preferred to be $1/2^{-}$ and $3/2^{-}$, respectively. From the present estimations, we also find the branching ratio of $\Lambda_c(3/2) \to \Sigma_c^\ast \pi$ is much larger than that of $\Lambda_c(1/2) \to \Sigma_c^\ast \pi$, thus $\Sigma_{c}^{*}\pi$ could be a good channel to distinguish the $J^{P}$ quantum numbers of $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$. Therefore, we suggest to searching for the structure in $\Sigma_{c}^{*}\pi$ invariant mass distribution in Belle $\amalg$.