Measurements of the branching fractions of the decays $B_s^0\to D_s^{\mp }{K}^{\pm }$ and $B_s^0\to D_s^{-}{\pi }^{+}$

The decay mode ${\text{B}}_s^0\to D_s^{\mp }{K}^{\pm }$ allows for one of the theoretically cleanest measurements of the CKM angle $\gamma$ through the study of time-dependent $\text{ensuremath}CP\text{xspace}$ violation. This paper reports a measurement of its branching fraction relative to the Cabibbo-favoured mode ${\text{B}}_s^0\to D_s^{-}{\pi }^{+}$ based on a data sample of 0.37 fb${}^{-1}$ proton-proton collisions at $\sqrt{s}=7$ TeV collected in 2011 with the LHCb detector. In addition, the ratio of $\text{ensuremath}\mathrm{B}\text{xspace}$ meson production fractions $\text{ensuremath}{f}_s\mathrm{/}{f}_d$, determined from semileptonic decays, together with the known branching fraction of the control channel $B^0\to D^{-}{\pi }^{+}$, is used to perform an absolute measurement of the branching fractions: $B (\B^0_s \to D^-s \pi^+) ;= (2.95 \pm 0.05 \pm 0.17^{,+,0.18}{,-,0.22}) \times 10^{-3}$,$B (\B^0_s \to D^\mp_s K^\pm) = (1.90 \pm 0.12 \pm 0.13^{,+,0.12}_{,-,0.14}) \times 10^{-4},$, where the first uncertainty is statistical, the second the experimental systematic uncertainty, and the third the uncertainty due to $f_s\mathrm{/}{f}_d$.