Determination of the branching fractions of $B_{s}^{0} \to D_{s}^{\mp} K^{\pm}$ and $B^{0} \to D_{s}^{-} K^{+}$

Abstract: Measurements are presented of the branching fractions of the decays $B_{s}^{0} \to D_{s}^{\mp} K^{\pm}$ and $B^{0} \to D_{s}^{-} K^{+}$ relative to the decays $B_{s}^{0} \to D_{s}^{-} \pi^{+}$ and $B^{0} \to D^{-} \pi^{+}$, respectively. The data used correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions. The ratios of branching fractions are $\dfrac{\mathcal{B}(B_{s}^{0} \to D_{s}^{\mp} K^{\pm})}{\mathcal{B}(B_{s}^{0} \to D_{s}^{-} \pi^{+})} = 0.0752 \pm 0.0015 \pm 0.0019$ and $\dfrac{\mathcal{B}(B^{0} \to D_{s}^{-} K^{+})}{\mathcal{B}(B^{0} \to D^{-} \pi^{+})} = 0.0129 \pm 0.0005 \pm 0.0008,$ where the uncertainties are statistical and systematic, respectively.