Observation of the suppressed ADS modes $B^{\pm }\to [\ddot{I}{€}^{\pm }{K}^{\mp }\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{K}^{\pm }$ and $B^{\pm }\to [\ddot{I}{€}^{\pm }{K}^{\mp }\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D\ddot{I}{€}^{\pm }$

Abstract

An analysis of $B^{\pm }\to D{K}^{\pm }$ and $B^{\pm }\to D\ddot{I}{€}^{\pm }$ decays is presented where the $D$ meson is reconstructed in the four-body final state $K^{\pm }\ddot{I}{€}^{\mp }\ddot{I}{€}^{+}\ddot{I}{€}^{-}$. Using LHCb data corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$, first observations are made of the suppressed ADS modes $B^{\pm }\to [\ddot{I}{€}^{\pm }{K}^{\mp }\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D{K}^{\pm }$ and $B^{\pm }\to [\ddot{I}{€}^{\pm }{K}^{\mp }\ddot{I}{€}^{+}\ddot{I}{€}^{-}{]}_D\ddot{I}{€}^{\pm }$ with a significance of $5.1\ddot{I}ƒ$ and greater than $10\ddot{I}ƒ$, 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 $B^{\pm }\to D{K}^{\pm }$ amplitudes is determined to be $r_B^K=0.097\pm 0.011$.

14 pages, 3 figures. Minor textual changes after journal acceptance