Measurement of $b$-hadron branching fractions for two-body decays into charmless charged hadrons

Based on data corresponding to an integrated luminosity of 0.37 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in 2011, the following ratios of branching fractions are measured: \begin{eqnarray*} \mathcal{B}\left(B^{0}\rightarrow\pi^{+}\pi^{-}\right) /\,\mathcal{B}\left(B^{0}\rightarrow K^+\pi^-\right) & = & 0.262\pm 0.009\pm 0.017,\\ (f_{s} / f_{d}) \cdot \mathcal{B}\left(B^{0}_{s}\rightarrow K^{+}K^{-}\right) /\, \mathcal{B}\left(B^{0}\rightarrow K^+\pi^-\right) & = & 0.316\pm 0.009\pm 0.019,\\ (f_{s} / f_{d}) \cdot \mathcal{B}\left(B^0_{s}\rightarrow\pi^+ K^-\right) /\, \mathcal{B}\left(B^{0}\rightarrow K^+\pi^-\right) & = & 0.074 \pm 0.006\pm 0.006,\\ (f_{d} / f_{s}) \cdot \mathcal{B}\left(B^{0} \rightarrow K^{+}K^{-}\right) /\, \mathcal{B}\left(B^{0}_s\rightarrow K^+K^-\right) & = & 0.018 \,^{+\,0.008}_{-\,0.007} \pm 0.009,\\ (f_{s} / f_{d}) \cdot \mathcal{B}\left(B^{0}_{s}\rightarrow \pi^{+}\pi^{-}\right) /\, \mathcal{B}\left(B^{0}\rightarrow \pi^+\pi^-\right) & = & 0.050 \,^{+\,0.011}_{-\,0.009} \pm 0.004,\\ \mathcal{B}\left(\Lambda^0_b\rightarrow p\pi^-\right) /\, \mathcal{B}\left(\Lambda^0_b\rightarrow pK^-\right) & = & 0.86 \pm 0.08\pm 0.05, \end{eqnarray*} where the first uncertainties are statistical and the second systematic. Using the current world average of $\mathcal{B}\left(B^{0}\rightarrow K^+\pi^-\right)$ and the ratio of the strange to light neutral $B$ meson production $f_s/f_d$ measured by LHCb, we obtain: \begin{eqnarray*} \mathcal{B}\left(B^{0}\rightarrow\pi^{+}\pi^{-}\right) & = & (5.08 \pm 0.17 \pm 0.37)\times 10^{-6},\\ \mathcal{B}\left(B^{0}_{s}\rightarrow K^{+}K^{-}\right) & = & (23.0 \pm 0.7 \pm 2.3)\times 10^{-6},\\ \mathcal{B}\left(B^0_{s}\rightarrow\pi^+ K^-\right) & = & (5.4 \pm 0.4 \pm 0.6)\times 10^{-6},\\ \mathcal{B}(B^0 \rightarrow K^+K^-) & = & (0.11 \,^{+\,0.05}_{-\,0.04} \pm 0.06)\times10^{-6},\\ \mathcal{B}(B^0_s \rightarrow \pi^+\pi^-) & = & (0.95 \,^{+\,0.21}_{-\,0.17} \pm 0.13)\times10^{-6}. \end{eqnarray*} The measurements of $\mathcal{B}\left(B^{0}_{s}\rightarrow K^{+}K^{-}\right)$, $\mathcal{B}\left(B^0_{s}\rightarrow\pi^+ K^-\right)$ and $\mathcal{B}(B^0 \rightarrow K^+K^-)$ are the most precise to date. The decay mode $B^0_s \rightarrow \pi^+\pi^-$ is observed for the first time with a significance of more than $5\sigma$.