Experimental constraints on the properties of $P_c$ states

Using new experimental data on photoproduction and $Λ_b^0$ decays, we derive 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 $Σ_c\bar D$, $Σ_c^*\bar D$ and $Σ_c\bar D^*$ molecules, but that $P_c(4457)$ does not fit into the same picture. Based on the apparent absence of additional partner states, and the striking disparity between $Λ_c^+\bar D^0$ and $Λ_c^+\bar D^{*0}$ decays, we conclude that $P_c(4440)$ has $3/2^-$ quantum numbers. Using heavy-quark symmetry we predict large experimental signals for $P_c$ states in $η_c p K^-$, $Λ_c^+\bar D^{*0}K^-$, and $Σ_c^{(*)}\bar D K^-$. We also argue that current experimental data on photoproduction is almost at the level of sensitivity required to observe $P_c$ states.

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