A study of $CP$ violation in $B^\mp \rightarrow Dh^\mp$ ($h=K,π$) with the modes $D \rightarrow K^\mp π^\pm π^0$, $D \rightarrow π^+π^-π^0$ and $D \rightarrow K^+K^-π^0$

Abstract

An analysis of the decays of $B^\mp \rightarrow D K^\mp$ and $B^\mp \rightarrow D π^\mp $ is presented in which the $D$ meson is reconstructed in the three-body final states $K^\mp π^\pm π^0$, $π^+ π^- π^0$ and $K^+ K^- π^0$. 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 $B^\mp \rightarrow [π^\mp K^\pm π^0]_D π^\mp$ and the quasi-GLW decay $B^\mp \rightarrow [K^+ K^- π^0]_D π^\mp$. The results are interpreted in the context of the unitarity triangle angle $γ$ and related parameters.