Measurement of the branching fractions of the decays $D^+\rightarrow K^-K ^+K^+$, $D^+\rightarrow \pi^-\pi^+K^+$ and $D^+_s\rightarrow \pi^-K^+K^+$

The branching fractions of the doubly Cabibbo-suppressed decays $D^+\rightarrow K^-K^+K^+$, $D^+\rightarrow \pi^-\pi^+K^+$ and $D^+_s\rightarrow\pi^-K^+K^+$ are measured using the decays $D^+\rightarrow K^-\pi^+\pi^+$ and $D^+_s\rightarrow K^-K^+\pi^+$ as normalisation channels. The measurements are performed using proton-proton collision data collected with the LHCb detector at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2.0 fb$^{-1}$. The results are \begin{align} \frac {\mathcal{B}(D^+\rightarrow K^-K^+K^+)} {\mathcal{B}(D^+\rightarrow K^-\pi^+\pi^+)}& = (6.541 \pm 0.025 \pm 0.042) \times 10^{-4},\nonumber \frac {\mathcal{B}(D^+\rightarrow \pi^-\pi^+K^+)} {\mathcal{B}(D^+\rightarrow K^-\pi^+\pi^+)}& = (5.231 \pm 0.009 \pm 0.023) \times 10^{-3}, \nonumber \frac {\mathcal{B}(D^+_s\rightarrow\pi^-K^+K^+)} {\mathcal{B}(D^+_s\rightarrow K^-K^+\pi^+)}& = (2.372 \pm 0.024 \pm 0.025) \times 10^{-3},\nonumber \end{align} where the uncertainties are statistical and systematic, respectively. These are the most precise measurements up to date.