Measurements of branching fraction ratios and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>asymmetries 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:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup></mml:math>decays in hadron collisions

We reconstruct ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}D{K}^{\ifmmode\pm\else\textpm\fi{}}$ decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity. We select decay modes where the $D$ meson decays to either ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ (flavor eigenstate) or ${K}^{\ensuremath{-}}{K}^{+}$, ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ ($CP$-even eigenstates), and measure the direct $CP$ asymmetry ${A}_{CP+}=0.39\ifmmode\pm\else\textpm\fi{}0.17(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.04(\mathrm{syst})$, and the double ratio of $CP$-even to flavor eigenstate branching fractions ${R}_{CP+}=1.30\ifmmode\pm\else\textpm\fi{}0.24(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.12(\mathrm{syst})$. These measurements will improve the determination of the Cabibbo-Kobayashi-Maskawa angle $\ensuremath{\gamma}$. They are performed here for the first time using data from hadron collisions.

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