We report a measurement of the indirect $CP$-violating asymmetries ($A_{\mathrm{\Gamma }}$) between effective lifetimes of anticharm and charm mesons reconstructed in $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ decays. We use the full data set of proton-antiproton collisions collected by the Collider Detector at Fermilab experiment and corresponding to $9.7{\mathrm{fb}}^{-1}$ of integrated luminosity. The strong-interaction decay $D^{*+}\to D^0{\pi }^{+}$ is used to identify the meson at production as $D^0$ or ${\overline{D}}^0$. We statistically subtract $D^0$ and ${\overline{D}}^0$ mesons originating from $b$-hadron decays and measure the yield asymmetry between anticharm and charm decays as a function of decay time. We measure $A_{\mathrm{\Gamma }}(K^{+}{K}^{-})=(-0.19\pm 0.15(\text{stat})\pm 0.04(\text{syst}))\%$ and $A_{\mathrm{\Gamma }}({\pi }^{+}{\pi }^{-})=(-0.01\pm 0.18(\text{stat})\pm 0.03(\text{syst}))\%$. The results are consistent with the hypothesis of $CP$ symmetry and their combination yields $A_{\mathrm{\Gamma }}=(-0.12\pm 0.12)\%$.

• Received 20 October 2014

DOI:https://doi.org/10.1103/PhysRevD.90.111103