Measurements of the branching fractions of Λc⁺→pπ⁻π⁺, Λc⁺→pK⁻K⁺, and Λc⁺→pπ⁻K⁺

The ratios of the branching fractions of the decays do Lambda(+)(c) -> , p pi(-)pi(+), Lambda(+->)(c) pK(-)K(+), and Lambda(+)(c) -> p pi K--(+) with respect to the Cabibbo-favoured Lambda(+)(c) -> pK(-)pi(+) decay are measured using proton-proton collision data collected with the LHCb experiment at a 7 TeV centre-of-mass energy and corresponding to an integrated luminosity of 1.0 fb(-1): B(Lambda(+)(c) -> p pi(-)pi(+))/B(Lambda(+)(c) -> pK(-)pi(+)) = (7.44 +/- 0.08 +/- 0.18)%. B(Lambda(+)(c) -> pK(-)K(+))/B(Lambda(+)(c) -> pK(-)pi(+) = (1.70 +/- 0.03 +/- 0.03)%, B(Lambda(+)(c) -> p pi(-)pi K-+(+))/B(Lambda(+)(c) -> pK(-)pi(+) = (0.165 +/- 0.015 +/- 0.005)%, where the uncertainties are statistical and systematic, respectively. These results are the most precise measurements of these quantities to date. When multiplied by the world average value for B(Lambda(+)(c) -> p pi(-)pi(+)), the corresponding branching fractions are B(Lambda(+)(c) -> p pi(-)pi(+) = (4.72 +/- 0.05 +/- 0.11 +/- 0.25) x 10(-3), B(Lambda(+)(c) -> pK(-)K(+)) = (1.08 +/- 0.02 +/- 0.02 +/- 0.06) x 10(-3), B(Lambda(+)(c) -> , p pi K--(+)) = (1.04 +/- 0.09 +/- 0.03 +/- 0.05) x 10(-4), where the final uncertainty is due to B(Lambda(+)(c) -> pK(-)pi(+)).