Study ofB−→DK−π+π−andB−→Dπ−π+π−decays and determination of the CKM angleγ

We report a study of the suppressed B− → DK−πþπ− and favored B− → Dπ−πþπ− decays, where the neutral D meson is detected through its decays to the K∓π and CP -even KþK− and πþπ− final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb−1. We observe the first significant signals in the CP - even final states of the D meson for both the suppressed B− → DK−πþπ− and favored B− → Dπ−πþπ− modes, as well as in the doubly Cabibbo suppressed D → Kþπ− final state of the B− → Dπ−πþπ− decay. Evidence for the suppressed decay B− → DK−πþπ−, with D → Kþπ−, is also presented. From the observed yields in the B− → DK−πþπ−, B− → Dπ−πþπ− and their charge conjugate decay modes, the most probable value of the weak phase γ corresponds to γ ¼ ð74þ20 −19 Þ°. This is one of the most precise single-measurement determinations of γ to date.