Study of $B^-\to DK^-π^+π^-$ and $B^-\to Dπ^-π^+π^-$ 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=(74-19+20)°. This is one of the most precise single-measurement determinations of γ to date.