Study of $B^{-}\to D{K}^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to D{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays and determination of the CKM angle $\gamma$

We report a study of the suppressed $B^{-}\to D{K}^{-}{\pi }^{+}{\pi }^{-}$ and favored $B^{-}\to D{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp }{\pi }^{\pm }$ and CP-even $K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}$ 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 $B^{-}\to D{K}^{-}{\pi }^{+}{\pi }^{-}$ and favored $B^{-}\to D{\pi }^{-}{\pi }^{+}{\pi }^{-}$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^{+}{\pi }^{-}$ final state of the $B^-\to D\pi^-\pi^+\pi^-$decay\mathrm{.}EvidencefortheADSsuppresseddecay$B^{-}\to DK^-\pi^+\pi^-$,with$D\to K^+\pi^-$, is also presented. From the observed yields in the $B^{-}\to D{K}^{-}{\pi }^{+}{\pi }^{-}$, $B^{-}\to D{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and their charge conjugate decay modes, we measure the value of the weak phase to be $\gamma =(74_{-19}^{+20}{)}^{\mathrm{o}}$. This is one of the most precise single-measurement determinations of $\gamma$ to date.