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.