  Within the chiral unitary approach and with the constraints of heavy quark
spin symmetry, we study the coupled channel interactions of ${\bar
D}^{(*)}\Sigma_c^{(*)}$ channels, close to whose thresholds three
pentaquark-like $P_c$ states have been reported by the LHCb Collaboration. In
the present work, we take into account the contributions of pion exchanges via
box diagrams to the interaction potentials, and therefore lift the degeneracy
in the masses of ${\bar D}^*\Sigma_c^{(*)}$ spin multiplets. Fitting the
$J/\psi p$ invariant mass distributions in the $\Lambda_b^0 \to J/\psi K^- p$
decay, we find that the LHCb pentaquark states can not be reproduced in the
direct $J/\psi p$ production in the $\Lambda_b^0$ decay, and can only be
indirectly produced in the final state interactions of the $\Lambda_b^0$ decay
products, ${\bar D}^*\Sigma_c^{(*)}$, which further supports the nature of
these states as $\bar{D}\Sigma_c$ molecules. Based on the fit results obtained,
we study the partial decay widths/branching ratios to other decay channels,
$\bar{D}^* \Lambda_c$, $\bar{D} \Lambda_c$, and $\eta_c N$, and the
corresponding invariant mass distributions. The resonances with
$J^P=\frac{1}{2}^-$, $P_c(4312)$, $P_c(4440)$ and the one of $\bar{D}^*
\Sigma_c^*$ around 4500 MeV, have large partial decay width into $\eta_c N$,
and thus, can be easily seen in the $\eta_c N$ invariant mass distributions. By
contrast, the states with $J^P=\frac{3}{2}^-$, $P_c(4457)$, the (predicted)
narrow $P_c(4380)$ and the bound state of $\bar{D}^* \Sigma_c^*$ with a mass of
about 4520 MeV, do not decay into $\eta_c N$. Therefore, the $\eta_c N$ channel
should be studied in future to provide further insights into the nature of
these states, especially that of the $P_c(4440)$ and $P_c(4457)$.
