Hidden-charm pentaquarks as a meson-baryon molecule with coupled channels for $\bar{D}^{(\ast)}\Lambda_{\rm c}$ and $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$

The recent observation of two hidden-charm pentaquark states by LHCb collaborations prompted us to investigate the exotic states close to the $\bar{D}\Lambda_{\rm c}$, $\bar{D}^{\ast}\Lambda_{\rm c}$, $\bar{D}\Sigma_{\rm c}$, $\bar{D}\Sigma^{\ast}_{\rm c}$, $\bar{D}^{\ast}\Sigma_{\rm c}$ and $\bar{D}^{\ast}\Sigma^{\ast}_{\rm c}$ thresholds. We therefore studied the hadronic molecules that form the coupled-channel system of $\bar{D}^{(\ast)}\Lambda_{\rm c}$ and $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$. As the heavy quark spin symmetry manifests the mass degenerations of $\bar{D}$ and $\bar{D}^\ast$ mesons, and of $\Sigma_{\rm c}$ and $\Sigma^\ast_{\rm c}$ baryons, the coupled channels of $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ are important in these molecules. In addition, we consider the coupling to the $\bar{D}^{(\ast)}\Lambda_{\rm c}$ channel whose thresholds are near the $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ thresholds, and the coupling to the state with nonzero orbital angular momentum mixed by the tensor force. This full coupled channel analysis of $\bar{D}^{(\ast)}\Lambda_{\rm c}-\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ with larger orbital angular momentum has never been performed before. By solving the coupled-channel Schr\"odinger equations with the one meson exchange potentials that respected to the heavy quark spin and chiral symmetries, we studied the hidden-charm hadronic molecules with $I(J^P)=1/2(3/2^\pm)$ and $1/2(5/2^\pm)$. We conclude that the $J^P$ assignment of the observed pentaquarks is $3/2^+$ for $P^+_{\rm c}(4380)$ and $5/2^-$ for $P^+_{\rm c}(4450)$, which is agreement with the results of the LHCb analysis. In addition, we give predictions for other $J^P=3/2^\pm$ states at 4136.0, 4307.9 and 4348.7 MeV in $J^P=3/2^-$, and 4206.7 MeV in $J^P=3/2^+$, which can be further investigated by means of experiment.