Measurements of the branching fractions of $Λ_{c}^{+} \rightarrow p π^{-} π^{+}$, $Λ_{c}^{+} \rightarrow p K^{-} K^{+}$, and $Λ_{c}^{+} \rightarrow p π^{-} K^{+}$
The ratios of the branching fractions of the decays $Λ_{c}^{+} \rightarrow p π^{-} π^{+}$, $Λ_{c}^{+} \rightarrow p K^{-} K^{+}$, and $Λ_{c}^{+} \rightarrow p π^{-} K^{+}$ with respect to the Cabibbo-favoured $Λ_{c}^{+} \rightarrow p K^{-} π^{+}$ 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$^{-1}$: \begin{align*} \frac{\mathcal{B}(Λ_{c}^{+} \rightarrow p π^{-} π^{+})}{\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})} & = (7.44 \pm 0.08 \pm 0.18)\,\%, \frac{\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} K^{+})}{\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})} &= (1.70 \pm 0.03 \pm 0.03)\,\%, \frac{\mathcal{B}(Λ_{c}^{+} \rightarrow p π^{-} K^{+})}{\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})} & = (0.165 \pm 0.015 \pm 0.005 )\,\%, \end{align*} 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 $\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$, the corresponding branching fractions are \begin{align*} \mathcal{B}(Λ_{c}^{+} \rightarrow p π^{-} π^{+}) &= (4.72 \pm 0.05 \pm 0.11 \pm 0.25) \times 10^{-3}, \mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} K^{+}) &= (1.08 \pm 0.02 \pm 0.02 \pm 0.06) \times 10^{-3}, \mathcal{B}(Λ_{c}^{+} \rightarrow p π^{-} K^{+}) &= (1.04 \pm 0.09 \pm 0.03 \pm 0.05) \times 10^{-4}, \end{align*} where the final uncertainty is due to $\mathcal{B}(Λ_{c}^{+} \rightarrow p K^{-} π^{+})$.