Measurement of Partial Widths and Search for Direct $CP$ Violation in $D^0$ Meson Decays to $K^{-}{K}^{+}$ and ${\pi }^{-}{\pi }^{+}$

We present a measurement of relative partial widths and decay rate $CP$ asymmetries in $K^{-}{K}^{+}$ and ${\pi }^{-}{\pi }^{+}$ decays of $D^0$ mesons produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. We use a sample of $2\times {10}^5$ $D^{*+}\to D^0{\pi }^{+}$ (and charge conjugate) decays with the $D^0$ decaying to $K^{-}{\pi }^{+}$, $K^{-}{K}^{+}$, and ${\pi }^{-}{\pi }^{+}$, corresponding to $123{\mathrm{pb}}^{-1}$ of data collected by the Collider Detector at Fermilab II experiment at the Fermilab Tevatron collider. No significant direct $CP$ violation is observed. We measure $\Gamma (D^0\to K^{-}{K}^{+})/\Gamma (D^0\to K^{-}{\pi }^{+})=0.0992\pm 0.0011\pm 0.0012$, $\Gamma (D^0\to {\pi }^{-}{\pi }^{+})/\Gamma (D^0\to K^{-}{\pi }^{+})=0.03594\pm 0.00054\pm 0.00040$, $A_{CP}(K^{-}{K}^{+})=(2.0\pm 1.2\pm 0.6)\%$, and $A_{CP}({\pi }^{-}{\pi }^{+})=(1.0\pm 1.3\pm 0.6)\%$, where, in all cases, the first uncertainty is statistical and the second is systematic.