On the hidden charm pentaquark-s in $\Lambda_b \to J/\psi K^- p$ decay

In a previous work we presented a theoretical analysis of the $\Lambda_b \to J/\psi K^- p$ reaction from where a recent experiment by the LHCb collaboration at CERN claimed the existence of two hidden charm pentaquarks, $P_c(4380)^+$ and $P_c(4450)^+$. In that work we focused only on the $\Lambda(1405)$ and $P_c(4450)^+$ signals and discussed the possible explanation of this pentaquark state within the picture of a dynamical meson-baryon molecule made up mostly from $\bar D^* \Sigma_c$ and $\bar D^* \Sigma^*_c$ components. In the present work we improve upon the previous one by considering the total $K^- p$ and $J/\psi p$ data including all the relevant resonances contributing to the spectra, and discuss the possible nature of both $P_c(4380)^+$ and $P_c(4450)^+$. We also discuss several important topics, like the effect of the contact term in the reaction, the viability of reproducing the data without the $P_c(4380)^+$ and the possible quantum numbers assignment to these pentaquarks.