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

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.