Measurements of the branching fractions of the decays Bs0 → Ds∓K± and Bs0 → Ds-π+

The decay mode B-s(0) -> (DsK +/-)-K--/+ allows for one of the theoretically cleanest measurements of the CKM angle gamma 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) -> D-s(-)pi(+) based on a data sample corresponding to 0.37 fb(-1) of proton-proton collisions at root s = 7TeV 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-pi(+), is used to perform an absolute measurement of the branching fractions: B (B-s(0) -> D-s(-)pi(+)) = (2.95 +/- 0.05 +/- 0.17(-0.22)(+0.18)) x 10(-3), B(B-s(0) -> (DK +/-)-K--/+) = (1.90 +/- 0.12 +/- 0.13(-0.14)(+0.12)) x 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).