Limits on $D^0\mathrm{\text{−}}{\overline{D}}^0$ Mixing and $CP$ Violation from the Ratio of Lifetimes for Decay to $K^{-}{\pi }^{+}$, $K^{-}{K}^{+}$, and ${\pi }^{-}{\pi }^{+}$

We present a measurement of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing parameters using the ratios of lifetimes extracted from samples of $D^0$ mesons decaying to $K^{-}{\pi }^{+}$, $K^{-}{K}^{+}$, and ${\pi }^{-}{\pi }^{+}$. Using $91{\mathrm{f}\mathrm{b}}^{-1}$ of data collected by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory, we obtain a value $Y=[0.8\pm 0.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\genfrac{}{}{0ex}{}{+0.5}{-0.4}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})]\%$, which, in the limit of $CP$ conservation, corresponds to the mixing parameter $y=\Delta \Gamma /2\Gamma$. Using the difference in lifetimes of $D^0$ and ${\overline{D}}^0$ mesons, we obtain the $CP$-violation parameter $\Delta Y=[-0.8\pm 0.6(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.})\pm 0.2(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.})]\%$.

Figure 1

The reconstructed $D^0$ mass distribution (points) superimposed on a projection of the mass fit (curve) for the four $D^0$ samples. The fit was performed within the restricted ranges of mass indicated by the vertical dotted lines. The portion of the sample assigned by the fit to the background is indicated by the shaded region.

Figure 2

The decay-time distribution for the four $D^0$ samples (points) within a $\pm 15\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ mass signal window superimposed on a projection of the lifetime fit (histogram). The shaded histogram is the portion of the sample assigned by the fit to the background. The points presented below the histograms are the difference between data and fit divided by the statistical error with error bars of unit length.