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