Pion radiative decays of excited hidden-charm pentaquark molecules: from $Σ_c^{(*)}\bar{D}^{(*)}(2S)$ molecules to the reported $P_c$ states

The discovery of the hidden-charm pentaquarks \(P_c(4312)\), \(P_c(4440)\) and \(P_c(4457)\) by the LHCb Collaboration are very likely to identify as the \(Σ_c^{(*)}\bar{D}^{(*)}\) molecules. A natural and crucial extension is the existence of excited molecular partners built from a ground-state cha