Measurements of the branching fractions of the decays $B^0_s to D^mp_s K^pm $ and $B^0_s to D^-_s +$

The decay mode B0s→D∓sK± 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 B0s→D−sπ+ based on a data sample of 0.37 fb−1 proton-proton collisions at s√=7 TeV collected in 2011 with the LHCb detector. In addition, the ratio of B meson production fractions fs/fd, determined from semileptonic decays, together with the known branching fraction of the control channel B0→D−π+, is used to perform an absolute measurement of the branching fractions: B(B0s→D−sπ+)\/=(2.95±0.05±0.17+0.18−0.22)×10−3, B(B0s→D∓sK±)=(1.90±0.12±0.13+0.12−0.14)×10−4, where the first uncertainty is statistical, the second the experimental systematic uncertainty, and the third the uncertainty due to fs/fd.