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A full amplitude analysis of $\Lambda_b^0 \to J/\psi p \pi^-$ decays isperformed with a data sample acquired with the LHCb detector from 7 and 8 TeV$pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$. Asignificantly better description of the data is achieved when, in addition tothe previously observed nucleon excitations $N\to p\pi^-$, either the$P_c(4380)^+$ and $P_c(4450)^+\to J/\psi p$ states, previously observed in$\Lambda_b^0 \to J/\psi p K^-$ decays, or the $Z_c(4200)^-\to J/\psi \pi^-$state, previously reported in $B^0 \to J/\psi K^+ \pi^-$ decays, or all three,are included in the amplitude models. The data support a model containing allthree exotic states, with a significance of more than three standarddeviations. Within uncertainties, the data are consistent with the$P_c(4380)^+$ and $P_c(4450)^+$ production rates expected from their previousobservation taking account of Cabibbo suppression.

Evidence for exotic hadron contributions to $\Lambda_b^0 \to J/\psi p \pi^-$ decays