Study of B^- → DK^-π⁺π^- and B^- → Dπ^-π⁺π^- decays and determination of the CKM angle γ

We report a study of the suppressed B^- → DK^-π⁺π^- and favored B^- → Dπ^-π⁺π^- decays, where the neutral D meson is detected through its decays to the K^∓π^± and CP -even K⁺K^- and π⁺π^- 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^-π⁺π^- and favored B^- → Dπ^-π⁺π^- modes, as well as in the doubly Cabibbo suppressed D → K⁺π^- final state of the B^- → Dπ^-π⁺π^- decay. Evidence for the suppressed decay B^- → DK^-π⁺π^-, with D → K⁺π^-, is also presented. From the observed yields in the B^- → DK^-π⁺π^-, B^- → Dπ^-π⁺π^- and their charge conjugate decay modes, the most probable value of the weak phase γ corresponds to γ=(74⁺²⁰_-19)°. This is one of the most precise single-measurement determinations of γ to date.