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Using new experimental data on photoproduction and $\Lambda_b^0$ decays, wederive constraints on the properties of the LHCb $P_c$ states. We conclude that$P_c(4312)$, $P_c(4380)$ and $P_c(4440)$ can be described as $\Sigma_c\bar D$,$\Sigma_c^*\bar D$ and $\Sigma_c\bar D^*$ molecules, but that $P_c(4457)$ doesnot fit into the same picture. Based on the apparent absence of additionalpartner states, and the striking disparity between $\Lambda_c^+\bar D^0$ and$\Lambda_c^+\bar D^{*0}$ decays, we conclude that $P_c(4440)$ has $3/2^-$quantum numbers. Using heavy-quark symmetry we predict large experimentalsignals for $P_c$ states in $\eta_c p K^-$, $\Lambda_c^+\bar D^{*0}K^-$, and$\Sigma_c^{(*)}\bar D K^-$. We also argue that current experimental data onphotoproduction is almost at the level of sensitivity required to observe $P_c$states.

Experimental constraints on the properties of $P_c$ states