Observation of the suppressed ADS modes $B^± \to [π^± K^∓ π^+π^-]_D K^±$ and $B^± \to [π^± K^∓ π^+π^-]_D π^±$

An analysis of B^± → DK^± and B^± → Dπ^± decays is presented where the D meson is reconstructed in the four^-body nal state K^±π^∓π⁺π-. Using LHCb data corresponding to an integrated luminosity of 1.0 fb^-1, rst observations are made of the suppressed ADS modes B^± →[π^±K^∓π⁺π-] D K^± and B^± → [π^±K^∓π⁺π-]Dπ^± with a signicance of 5.1σ and greater than 10σ, respectively. Measurements of CP asymmetries and CP^-conserving ratios of partial widths from this family of decays are also performed. The magnitude of the ratio between the suppressed and favoured B^± → DK^± amplitudes is determined to be r^K<inf>B</inf> = 0.097±0.011. © CERN for the benet of the LHCb Collaboration.