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Measurement of the branching fraction and decay rate asymmetry of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:mrow></mml:msub><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:…
We report the observation of the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}}{K}^{\ensuremath{-}}$, where ${D}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}}$ indicates a neutral $D$ meson detected in the final state ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$, excluding ${K}_{S}^{0}{\ensuremath{\pi}}^{0}$. This doubly Cabibbo-suppressed decay chain can be used to measure the CKM phase $\ensuremath{\gamma}$. Using about $229\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}B\overline{B}$ events recorded by the BABAR experiment at the PEP-II …