$J/\psi N$ interactions revisited and $\Lambda_b^0 \to J/\psi K^- (\pi^-) p$ decays

Recently LHCb experiments confirmed the findings of the two $P_c$ states in the $\Lambda_b^0 \to J/\psi p \pi^-$ decays. In the present work, we investigate both the $\Lambda_b^0 \to J/\psi K^- p$ and the $\Lambda_b^0 \to J/\psi p \pi^-$ decays, continuing the investigations of our former works on the interactions of $J/\psi N$ with its coupled channels by considering the s-/u- channel contributions. We obtain consistent results of the line-shape of the $J/\psi N$ invariant mass distribution with the LHCb experiments, and favour the $P_c (4450)$ state as a $\bar{D}^* \Sigma_c$ bound state with $J=1/2^-$.