Measurement of $CP$-violating asymmetries in $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays at CDF

We report on a measurement of $CP$-violating asymmetries ($A_{CP}$) in the Cabibbo-suppressed $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays reconstructed in a data sample corresponding to $5.9{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the upgraded Collider Detector at Fermilab. We use the strong decay $D^{*+}\to D^0{\pi }^{+}$ to identify the flavor of the charmed meson at production and exploit $CP$-conserving strong $c\overline{c}$ pair production in $p\overline{p}$ collisions. High-statistics samples of Cabibbo-favored $D^0\to K^{-}{\pi }^{+}$ decays with and without a $D^{*\pm }$ tag are used to correct for instrumental effects and significantly reduce systematic uncertainties. We measure $A_{CP}(D^0\to {\pi }^{+}{\pi }^{-})=(+0.22\pm 0.24(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$ and $A_{CP}(D^0\to K^{+}{K}^{-})=(-0.24\pm 0.22(\mathrm{stat})\pm 0.09(\mathrm{syst}))\%$, in agreement with $CP$ conservation. These are the most precise determinations from a single experiment to date. Under the assumption of negligible direct $CP$ violation in $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays, the results provide an upper limit to the $CP$-violating asymmetry in $D^0$ mixing, $|A_{CP}^{\mathrm{ind}}(D^0)|<0.13\%$ at the 90% confidence level.