Determination of f_s/f_d for 7 TeV pp collisions and a measurement of the branching fraction of the decay Bd->D-K+

The relative abundance of the three decay modes $B_d\to D^{-}{K}^{+}$, $B_d \to D^- \pi^+$and$B_s \to D_s^- \pi^+$producedin7TeV$pp$ collisions at the LHC is determined from data corresponding to an integrated luminosity of 35 pb${}^{-1}$. The branching fraction of $B_d\to D^{-}{K}^{+}$ is found to be $\cal B (B_d \to D^- K^+) = (2.01 \pm 0.18^{$\text{stat}$} \pm 0.14^{$\text{syst}$})\times 10^{-4}$. The ratio of fragmentation fractions \fsfdt is determined through the relative abundance of $B_s\to D_s^{-}{\pi }^{+}$ to $B_d\to D^{-}{K}^{+}$ and $B_d\to D^{-}{\pi }^{+}$, leading to $f_s/f_d = 0.253 \pm 0.017 \pm 0.017 \pm 0.020$, where the uncertainties are statistical, systematic, and theoretical respectively.