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