Measurement of the Cabibbo-Kobayashi-Maskawa Angle<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math>in<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:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>∓</mml:mo></mml:msup></mml:math>Decays with a Dalitz Analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>→</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup><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:math>

We report on a measurement of the Cabibbo-Kobayashi-Maskawa $CP$-violating phase $\ensuremath{\gamma}$ through a Dalitz analysis of neutral $D$ decays to ${K}_{S}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ in the processes ${B}^{\ensuremath{\mp}}\ensuremath{\rightarrow}{D}^{(*)}{K}^{\ensuremath{\mp}}$, ${D}^{*}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{0}$, $D\ensuremath{\gamma}$. Using a sample of $227\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected by the BABAR detector, we measure the amplitude ratios ${r}_{B}=0.12\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.03\ifmmode\pm\else\textpm\fi{}0.04$ and ${r}_{B}^{*}=0.17\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.03\ifmmode\pm\else\textpm\fi{}0.03$, the relative strong phases ${\ensuremath{\delta}}_{B}=(104\ifmmode\pm\else\textpm\fi{}{45}_{\ensuremath{-}21\ensuremath{-}24}^{+17+16})\ifmmode^\circ\else\textdegree\fi{}$ and ${\ensuremath{\delta}}_{B}^{*}=(\ensuremath{-}64\ifmmode\pm\else\textpm\fi{}{41}_{\ensuremath{-}12}^{+14}\ifmmode\pm\else\textpm\fi{}15)\ifmmode^\circ\else\textdegree\fi{}$ between the amplitudes $\mathcal{A}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{(*)0}{K}^{\ensuremath{-}})$ and $\mathcal{A}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{(*)0}{K}^{\ensuremath{-}})$, and $\ensuremath{\gamma}=(70\ifmmode\pm\else\textpm\fi{}{31}_{\ensuremath{-}10\ensuremath{-}11}^{+12+14})\ifmmode^\circ\else\textdegree\fi{}$. The first error is statistical, the second is the experimental systematic uncertainty, and the third reflects the Dalitz model uncertainty. The results for the strong and weak phases have a twofold ambiguity.

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