Observation of the suppressed ADS modes B^\pm \to (\pi^\pm K^\pm \pi^+^\pi^-)_D K^\pm and B^\pm \to (\pi^\pm K^\pm \pi^+^\pi^-)_D \pi^\pm

An analysis of B±→DK± and B±→Dπ± decays is presented where the D meson is reconstructed in the four-body final state K±π∓π+π−. Using LHCb data corresponding to an integrated luminosity of , first observations are made of the suppressed ADS modes B±→[π±K∓π+π−]DK± and B±→[π±K∓π+π−]Dπ± with a significance 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 .