Measurement of $CP$ Asymmetries in $D^0 \to h^+h^-$ Decays with the CDF Detector

The CDF experiment has now collected more than 4 fb$^{-1}$ of data and has access to the largest samples of $D^{*+}\to D^0 \pi^{+}$ decays currently available where $D^0$ decays as $D^0\rightarrow h^+h^-$ (with $h=K$ or $\pi$). Measurements of decay rates in these channels are sensitive to $CP$~violation and flavor mixing in the charm sector but require a careful analysis to separate signals from one another and from the background with the needed accuracy. We use a multivariate likelihood fit that combines kinematic and particle identification information to accurately determine the composition of the sample in terms of Cabibbo-favored, Cabibbo-suppressed and doubly-Cabibbo-suppressed decays. We apply this technique to a precision measurement of direct $CP$~violating asymmetries in $D^{0}\to \pi^{+}\pi^{-}$ and $D^{0}\to K^{+}K^{-}$ decays.