Measurement of $C\!P$ observables in $B^\pm \rightarrow D K^\pm$ and $B^\pm \rightarrow D π^\pm$ with two- and four-body $D$ decays
Measurements of $C\!P$ observables in $B^\pm \rightarrow D K^\pm$ and $B^\pm \rightarrow D π^\pm$ decays are presented where the $D$ meson is reconstructed in the final states $K^\pmπ^\mp$, $π^\pm K^\mp$, $K^+K^-$, $π^+π^-$, $K^\pmπ^\mp π^+ π^-$, $π^\pm K^\mp π^+ π^-$ and $π^+ π^- π^+ π^-$. This analysis uses a sample of charged $B$ mesons from $pp$ collisions collected by the LHCb experiment in 2011 and 2012, corresponding to an integrated luminosity of 3.0 fb$^{-1}$. Various \CP-violating effects are reported and together these measurements provide important input for the determination of the unitarity triangle angle $γ$. The analysis of the four-pion $D$ decay mode is the first of its kind.