The Cabibbo-suppressed decay $Lambda^0_brightarrowpsi(2S)ppi^-$ is observed for the first time using a data sample collected by the LHCb experiment in proton-proton collisions corresponding to 1.0, 2.0 and 1.9fb$^{-1}$ of integrated luminosity at centre-of-mass energies of 7, 8 and 13TeV, respectively. The $psi(2S)$ mesons are reconstructed in the $mu^+mu^-$ final state. The~branching fraction with respect to that of the $Lambda^0_brightarrowpsi(2S)pK^-$ decay mode is measured to be $$frac{mathcal{B}left(Lambda^0_brightarrowpsi(2S)ppi^- right)} {mathcal{B}left(Lambda^0_brightarrowpsi(2S)pK^-right)}=left(11.4 pm 1.3 pm 0.2right)!%,,$$ where the first uncertainty is statistical and the second is systematic. The $psi(2S)p$ and $psi(2S)pi^-$ mass spectra are investigated and no evidence for exotic resonances is found.
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