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

The ratios of the branching fractions of the decays Λ _c ⁺  → pπ⁻π⁺, Λ _c ⁺  → pK⁻K⁺, and Λ _c ⁺  → pπ⁻K⁺ with respect to the Cabibbo-favoured Λ _c ⁺  → pK⁻π⁺ 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(Λ+c→pπ−π+)B(Λ+c→pK−π+)=(7.44±0.08±0.18)%,B(Λ+c→pK−K+)B(Λ+c→pK−π+)=(1.70±0.03±0.03)%B(Λ+c→pπ−K+)B(Λ+c→pK−π+)=(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(Λ+c→pK−π+), the corresponding branching fractions are B(Λ+c→pπ−π+)=(4.72±0.05±0.11±0.25)×10−3,B(Λ+c→pK−K+)=(1.08±0.02±0.02±0.06)×10−3,B(Λ+c→pπ−K+)=(1.04±0.09±0.03±0.05)×10−4, where the final uncertainty is due to B(Λ+c→pK−π+).