A full amplitude analysis of $Lambda_b^0 to J/psi p pi^-$ decays is performed with a data sample acquired with the LHCb detector from 7 and 8 TeV $pp$ collisions, corresponding to an integrated luminosity of 3 fb$^{-1}$. A significantly better description of the data is achieved when, in addition to the previously observed nucleon excitations $Nto ppi^-$, 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 all three exotic states, with a significance of more than three standard deviations. Within uncertainties, the data are consistent with the $P_c(4380)^+$ and $P_c(4450)^+$ production rates expected from their previous observation taking account of Cabibbo suppression.
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