First Observation of the Decays B¯⁰ → D⁺K^-π⁺π^- and B^- → D⁰K^-π⁺π^-

First observations of the Cabibbo-suppressed decays B¯ ⁰ → D ⁺K ^-π ⁺π ^- and B ^- → D ⁰K ^-π ⁺π ^- are reported using 35 pB ^-1 of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo-favored decays, from which we obtain B(B¯ ⁰→ D ⁺K ^-π ⁺π ^-)/B(B¯ ⁰→D ⁺π ^-π ⁺π ^-)=(5.9±1.1±0.5)×10 ^-2 and B(B ^-→D ⁰K ^-π ⁺π ^-)/B(B ^-→ D ⁰π ^-π ⁺π ^-)=(9.4±1.3±0.9)×10 ^-2, where the uncertainties are statistical and systematic, respectively. The B ^- → D ⁰K ^-π ⁺π ^- decay is particularly interesting, as it can be used in a similar way to B ^- → D ⁰K ^- to measure the Cabibbo-Kobayashi-Maskawa phase γ.