The Cabibbo-suppressed decay $Lambda_b^0rightarrowchi_{c1}ppi^-$ is observed for the first time using data from proton-proton collisions corresponding to an integrated luminosity of 6fb$^{-1}$, collected with the LHCb detector at a centre-of-mass energy of 13TeV. Evidence for the $Lambda_b^0rightarrowchi_{c2}ppi^-$ decay is also found. Using the $Lambda_b^0rightarrowchi_{c1}pK^-$ decay as normalisation channel, the ratios of branching fractions are measured to be $$begin{array}{rcl} frac{ mathcal{B} (Lambda_b^0rightarrowchi_{c1}ppi^-)}{mathcal{B} (Lambda_b^0rightarrowchi_{c1}pK^-)} & = & (6.59 pm 1.01 pm 0.22 ) times 10^{-2} ,, frac{mathcal{B} (Lambda_b^0rightarrowchi_{c2}ppi^-)}{mathcal{B} (Lambda_b^0rightarrowchi_{c1}ppi^-)} & = & 0.95 pm 0.30 pm 0.04 pm 0.04 ,, frac{mathcal{B} (Lambda_b^0rightarrowchi_{c2}pK^-)}{mathcal{B} (Lambda_b^0rightarrowchi_{c1}pK^-)} & = & 1.06 pm 0.05 pm 0.04 pm 0.04 ,,end{array}$$ where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainties in the branching fractions of $chi_{c1,2}rightarrow J/psigamma$ decays.
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