Exploring Bs → Ds(*)±K∓ decays in the presence of a sizable width difference ΔΓs

The B-s -> D-s(()*K-)+/-(-/+) decays allow a theoretically clean determination of phi(s) + gamma, where phi(s) is the B-s(0)-(B) over bar (0)(s) mixing phase and gamma the usual angle of the unitarity triangle. A sizable B-s decay width difference Delta Gamma(s) was recently established, which leads to subtleties in analyses of the B-s -> D-s(()*K-)+/-(-/+) branching ratios but also offers new "untagged" observables, which do not require a distinction between initially present B-s(0) or (B) over bar (0)(s) mesons. We clarify these effects and address recent measurements of the ratio of the B-s -> (DsK -/+)-K-+/-, B-s -> D-s(+/-)pi(-/+) branching ratios. In anticipation of future LHCb analyses, we apply the SU(3) flavour symmetry of strong interactions to convert the B-factory data for B-d -> D-(*()+/-)pi(-/+) , B-d -> D-s(+/-)pi(-/+) decays into predictions of the B-s -> D-s(()*K-)+/-(-/+) observables, and discuss strategies for the extraction of phi(s) + gamma, with a special focus on untagged observables and the resolution of discrete ambiguities. Using our theoretical predictions as a guideline, we make simulations to estimate experimental sensitivities, and extrapolate to the end of the planned LHCb upgrade. We find that the interplay between the untagged observables, which are accessible thanks to the sizable Delta Gamma(s), and the mixing-induced CP asymmetries, which require tagging, will play the key role for the experimental determination of phi(s) + gamma. (C) 2012 Elsevier B.V. All rights reserved.