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$^{+}$ → K$^{−}$K$^{+}$K$^{+}$, D$^{+}$ → π$^{−}$π$^{+}$K$^{+}$ and D$_{s}^{+}$ → π$^{−}$K$^{+}$K$^{+}$ are measured using the decays D$^{+}$ → K$^{−}$π$^{+}$π$^{+}$ and D$_{s}^{+}$ → K$^{−}$K$^{+}$π$^{+}$ 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{array}{c}\hfill \frac{\mathrm{\mathcal{B}}\left({D}^{+}\to {K}^{-}{K}^{+}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({D}^{+}\to {K}^{-}{\pi}^{+}{\pi}^{+}\right)} = \left(6.541\pm 0.025\pm 0.042\right)\times {10}^{-4},\hfill \\ {}\hfill \frac{\mathrm{\mathcal{B}}\left({D}^{+}\to\ {\pi}^{-}{\pi}^{+}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({D}^{+}\to {K}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(5.231\pm 0.009\pm 0.023\right)\times {10}^{-3},\hfill \\ {}\hfill \frac{\mathrm{\mathcal{B}}\left({D}_s^{+}\to\ {\pi}^{-}{K}^{+}{K}^{+}\right)}{\mathrm{\mathcal{B}}\left({D}_s^{+}\to {K}^{-}{K}^{+}{\pi}^{+}\right), } = \left(2.372\pm 0.024\pm 0.025\right)\times {10}^{-3},\hfill \end{array} $