A study of $CP$ violation in $B^{\mp }\to D{h}^{\mp }$ ($h=K,\ddot{I}€$) with the modes $D\to K^{\mp }\ddot{I}{€}^{\pm }\ddot{I}{€}^0$, $D\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $D\to K^{+}{K}^{-}\ddot{I}{€}^0$

Abstract

An analysis of the decays of $B^{\mp }\to D{K}^{\mp }$ and $B^{\mp }\to D\ddot{I}{€}^{\mp }$ is presented in which the $D$ meson is reconstructed in the three-body final states $K^{\mp }\ddot{I}{€}^{\pm }\ddot{I}{€}^0$, $\ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $K^{+}{K}^{-}\ddot{I}{€}^0$. Using data from LHCb corresponding to an integrated luminosity of 3.0 fb${}^{-1}$ of $pp$ collisions, measurements of several $CP$ observables are performed. First observations are obtained of the suppressed ADS decay $B^{\mp }\to [\ddot{I}{€}^{\mp }{K}^{\pm }\ddot{I}{€}^0{]}_D\ddot{I}{€}^{\mp }$ and the quasi-GLW decay $B^{\mp }\to [K^{+}{K}^{-}\ddot{I}{€}^0{]}_D\ddot{I}{€}^{\mp }$. The results are interpreted in the context of the unitarity triangle angle ${\hat{I}}^3$ and related parameters.