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

An analysis of $B^{\pm}\to DK^{\pm}$ and $B^{\pm}\to Dπ^{\pm}$ decays is presented where the $D$ meson is reconstructed in the four-body final state $K^{\pm}π^{\mp} π^+ π^-$. Using LHCb data corresponding to an integrated luminosity of $1.0{\rm \,fb}^{-1}$, first observations are made of the suppressed ADS modes $B^{\pm}\to [π^{\pm} K^{\mp}π^+π^-]_D K^{\pm}$ and $B^{\pm}\to [π^{\pm} K^{\mp} π^+π^- ]_Dπ^{\pm}$ 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 $B^{\pm}\to DK^{\pm}$ amplitudes is determined to be $r^K_B = 0.097 \pm{0.011}$.