We develop a model for the production of the P c states observed at LHCb in Λ b → J/ψ p K − decays. With fewer parameters than other approaches, we obtain excellent fits to the J/ψ p invariant mass spectrum, capturing both the prominent peaks, and broader features over the full range of invariant mass. A distinguishing feature of our model is that whereas P c ( 4312), P c (4380) and P c (4440) are resonances with Σ ( * ) c D( * ) constituents, the nature of P c (4457) is quite different, and can be understood either as a Σ c D * threshold cusp, a Λ c (2595) D enhancement due to the triangle singularity, or a Λ c (2595) D resonance. We propose experimental measurements that can discriminate among these possibilities. Unlike in other models, our production mechanism respects isospin symmetry and the empirical dominance of colour-enhanced processes in weak decays, and additionally gives a natural explanation for the overall shape of the data. Our model is consistent with experimental constraints from photoproduction and Λ b → Λ c D( * )0 K − decays and it does not imply the existence of partner states whose apparent absence in experiments is unexplained in other models.

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