Search for $D^0\mathrm{\text{−}}{\overline{D}}^0$ Mixing and a Measurement of the Doubly Cabibbo-Suppressed Decay Rate in $D^0\to K\pi$ Decays

We present results of a search for $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing and a measurement of $R_{\mathrm{D}}$, the ratio of doubly Cabibbo-suppressed decays to Cabibbo-favored decays, using $D^0\to K^{+}{\pi }^{-}$ decays from $57.1{\mathrm{f}\mathrm{b}}^{-1}$ of data collected near $\sqrt{s}=10.6\mathrm{G}\mathrm{e}\mathrm{V}$ with the BABAR detector at the PEP-II collider. At the $95\%$ confidence level, allowing for $CP$ violation, we find the mixing parameters $x^{\prime 2}<0.0022$ and $-0.056<y^{\prime }<0.039$, and the mixing rate $R_{\mathrm{M}}<0.16\%$. In the limit of no mixing, $R_{\mathrm{D}}=[0.357\pm 0.022(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.027(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\%$ and the $CP$-violating asymmetry $A_{\mathrm{D}}=0.095\pm 0.061(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.083(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$.

Figure 1

The distribution of the WS data for (a) $m_{K\pi }$ with $144.5<\delta m<146.5\mathrm{M}\mathrm{e}\mathrm{V}/c^2$, (b) $\delta m$ with $|m_{K\pi }-m_{D^0}|<20\mathrm{M}\mathrm{e}\mathrm{V}/c^2$, (c) $m_{K\pi }$ with $150<\delta m<165\mathrm{M}\mathrm{e}\mathrm{V}/c^2$, and (d) $\delta m$ with $25<|m_{K\pi }-m_{D^0}|<60\mathrm{M}\mathrm{e}\mathrm{V}/c^2$. Data are shown as points with the contributions from the fit overlaid: signal (open), unassociated pion background (dark shaded), double misidentification background (black), and combinatorial background (light shaded).

Figure 2

The proper time distribution for the WS candidates in (a) the signal region ($73\%$ signal purity) and (b) a background region ($50\%$ combinatorial background). See Fig. 1 for component definitions.

Figure 3

$95\%$ C.L. limits in $x^{\prime 2},y^{\prime }$ with and without $CP$ violation (CPV) allowed. The solid point represents the most likely fit point assuming $CP$ conservation and the open circle the same but allowing $CP$ violation and forcing $x^{\prime 2}>0$. The dotted (dashed) line is the statistical (statistical and systematic) contour for the case where no $CP$ violation is allowed. The solid and dash-dotted lines are for the corresponding case where $CP$ violation is allowed.