Observation of the suppressed ADS modes B±→[π±K∓π+π−]DK± and B±→[π±K∓π+π−]Dπ±

An analysis of and B-+/- -> DK +/- and B-+/- -> D pi(+/-) decays is presented where the D meson is reconstructed in the four-body final state K-+/-pi(-/+)pi(+)pi(-). Using LHCb data corresponding to an integrated luminosity of 1.0 fb(-1), first observations are made of the suppressed ADS modes B-+/- ->[pi K-+/-(-/+)pi(+)pi(-)](D)K-+/- and B +/- -> [pi K-+/-(-/+)pi(+)pi(-)](D)pi(+/-) with a significance of 5.1 sigma and greater than 10 sigma, 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(B)(K) …