Search for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mo>→</mml:mo><mml:mi>u</mml:mi></mml:math>transitions 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:mi>D</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>decays

We report results from an updated study of the suppressed decays ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}D{K}^{\ensuremath{-}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{*}{K}^{\ensuremath{-}}$ followed by $D\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, where ${D}^{(*)}$ indicates a ${D}^{(*)0}$ or a ${\overline{D}}^{(*)0}$ meson, and ${D}^{*}\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{0}$ or ${D}^{*}\ensuremath{\rightarrow}D\ensuremath{\gamma}$. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity triangle angle $\ensuremath{\gamma}$ due to interference between the $b\ensuremath{\rightarrow}c$ transition ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{(*)0}{K}^{\ensuremath{-}}$ followed by the doubly Cabibbo-suppressed decay ${D}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, and the $b\ensuremath{\rightarrow}u$ transition ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{(*)0}{K}^{\ensuremath{-}}$ followed by the Cabibbo-favored decay ${\overline{D}}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. We also report an analysis of the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{(*)}{\ensuremath{\pi}}^{\ensuremath{-}}$ with the $D$ decaying into the doubly Cabibbo-suppressed mode $D\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. Our results are based on $467\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected with the BABAR detector at SLAC. We measure the ratios ${\mathcal{R}}^{(*)}$ of the suppressed ($[{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{]}_{D}{K}^{\ensuremath{-}}/{\ensuremath{\pi}}^{\ensuremath{-}}$) to favored ($[{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{]}_{D}{K}^{\ensuremath{-}}/{\ensuremath{\pi}}^{\ensuremath{-}}$) branching fractions as well as the $CP$ asymmetries ${\mathcal{A}}^{(*)}$ of those modes. We see indications of signals for the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}D{K}^{\ensuremath{-}}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}_{D{\ensuremath{\pi}}^{0}}^{*}{K}^{\ensuremath{-}}$ suppressed modes, with statistical significances of 2.1 and $2.2\ensuremath{\sigma}$, respectively, and we measure: ${\mathcal{R}}_{DK}=(1.1\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2},\phantom{\rule{2em}{0ex}}{\mathcal{A}}_{DK}=\ensuremath{-}0.86\ifmmode\pm\else\textpm\fi{}{0.47}_{\ensuremath{-}0.16}^{+0.12}$, ${\mathcal{R}}_{(D{\ensuremath{\pi}}^{0})K}^{*}=(1.8\ifmmode\pm\else\textpm\fi{}0.9\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2},\phantom{\rule{2em}{0ex}}{\mathcal{A}}_{(D{\ensuremath{\pi}}^{0})K}^{*}=+0.77\ifmmode\pm\else\textpm\fi{}0.35\ifmmode\pm\else\textpm\fi{}0.12,\phantom{\rule{2em}{0ex}}{\mathcal{R}}_{(D\ensuremath{\gamma})K}^{*}=(1.3\ifmmode\pm\else\textpm\fi{}1.4\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2},{\mathcal{A}}_{(D\ensuremath{\gamma})K}^{*}=+0.36\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}{0.94}_{\ensuremath{-}0.41}^{+0.25}$, where the first uncertainty is statistical and the second is systematic. We use a frequentist approach to obtain the magnitude of the ratio ${r}_{B}\ensuremath{\equiv}|A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{0}{K}^{\ensuremath{-}})/A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{0}{K}^{\ensuremath{-}})|=({9.5}_{\ensuremath{-}4.1}^{+5.1})%$, with ${r}_{B}<16.7%$ at 90% confidence level. In the case of ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{*}{K}^{\ensuremath{-}}$ we find ${r}_{B}^{*}\ensuremath{\equiv}|A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{D}}^{*0}{K}^{\ensuremath{-}})/A({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{*0}{K}^{\ensuremath{-}})|=({9.6}_{\ensuremath{-}5.1}^{+3.5})%$, with ${r}_{B}^{*}<15.0%$ at 90% confidence level.

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