Measurements of the branching fractions of the decays $B^{0}_{s} to D^{mp}_{s} K^{pm} $ and $B^{0}_{s} to D^{-}_{s} pi^{+}$

The decay mode $B^{0}_{s} to D^{mp}_{s} K^{pm} $ allows for one of the theoretically cleanest measurements of the CKM angle $gamma$ through the study of time-dependent $ensuremath{CP}xspace$ violation. This paper reports a measurement of its branching fraction relative to the Cabibbo-favoured mode $B^{0}_{s} to D^{-}_{s} pi^{+}$ 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 $ensuremath{mathrm{B}}xspace$ meson production fractions $ensuremath{f_s/f_d}$, 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 $f_s/f_d$.