Study of $B^{-}to DK^-pi^+pi^-$ and $B^-to Dpi^-pi^+pi^-$ decays and determination of the CKM angle $gamma$

We report a study of the suppressed $B^-to DK^-pi^+pi^-$ and favored $B^-to Dpi^-pi^+pi^-$ 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 $B^-to DK^-pi^+pi^-$ and favored $B^-to Dpi^-pi^+pi^-$ modes, as well as in the doubly Cabibbo-suppressed $Dto K^+pi^-$ final state of the $B^-to Dpi^-pi^+pi^-$ decay. Evidence for the ADS suppressed decay $B^{-}to DK^-pi^+pi^-$, with $Dto K^+pi^-$, is also presented. From the observed yields in the $B^-to DK^-pi^+pi^-$, $B^-to Dpi^-pi^+pi^-$ and their charge conjugate decay modes, we measure the value of the weak phase to be $gamma=(74^{+20}_{-19})^{rm o}$. This is one of the most precise single-measurement determinations of $gamma$ to date.