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

Abstract: The relative abundance of the three decay modes $B_d \to D^- K^+$, $B_d \to D^- \pi^+$ and $B_s \to D_s^- \pi^+$ produced in 7 TeV $pp$ 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 $\cal B (B_d \to D^- K^+) = (2.01 \pm 0.18^{\textrm{stat}} \pm 0.14^{\textrm{syst}})\times 10^{-4}$. 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.