Lifetime differences, direct $\mathrm{CP}$ violation, and partial widths in $D^0$ meson decays to $K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}$

We describe several measurements using the decays $D^0\to K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}.$ We find the ratio of partial widths, $\Gamma {(D}^0\to K^{+}{K}^{-})/\Gamma {(D}^0\to {\pi }^{+}{\pi }^{-}),$ to be $2.96\pm 0.16\pm 0.15,$ where the first error is statistical and the second is systematic. We observe no evidence for direct $\mathrm{CP}$ violation, obtaining $A_{\mathrm{CP}}\mathrm{}\left(\mathrm{KK}\right)=(0.0\mathrm{}\pm 2.2\pm 0.8)\%$ and $A_{\mathrm{CP}}\left(\pi \pi \right)=(1.9\mathrm{}\pm 3.2\pm 0.8)\%.$ In the limit of no $\mathrm{CP}$ violation we measure the mixing parameter $y_{\mathrm{CP}}=-0.012\pm 0.025\pm 0.014$ by measuring the lifetime difference between $D^0\to K^{+}{K}^{-}$ or ${\pi }^{+}{\pi }^{-}$ and the $\mathrm{CP}$ neutral state, $D^0\to K^{-}{\pi }^{+}.$ We see no evidence for mixing.