Measurement of $D^0\mathrm{\text{−}}{\overline{D}}^0$ Mixing Parameters Using $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and $D^0\to K_S^0{K}^{+}{K}^{-}$ Decays

We report a direct measurement of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing parameters through a time-dependent amplitude analysis of the Dalitz plots of $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and, for the first time, $D^0\to K_S^0{K}^{+}{K}^{-}$ decays. The low-momentum pion ${\pi }_s^{+}$ in the decay $D^{*+}\to D^0{\pi }_s^{+}$ identifies the flavor of the neutral $D$ meson at its production. Using $468.5{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ colliding-beam data recorded near $\sqrt{s}=10.6\mathrm{GeV}$ by the BABAR detector at the PEP-II asymmetric-energy collider at SLAC, we measure the mixing parameters $x=[1.6\pm 2.3(\mathrm{stat})\pm 1.2(\mathrm{syst})\pm 0.8(\mathrm{model})]\times {10}^{-3}$, and $y=[5.7\pm 2.0(\mathrm{stat})\pm 1.3(\mathrm{syst})\pm 0.7(\mathrm{model})]\times {10}^{-3}$. These results provide the best measurement to date of $x$ and $y$. The knowledge of the value of $x$, in particular, is crucial for understanding the origin of mixing.

Figure 1

Distributions of $m_{D^0}\mathrm{\text{−}}\Delta m$ for (a) $K_S^0{\pi }^{+}{\pi }^{-}$ and (b) $K_S^0{K}^{+}{K}^{-}$ data after all selection criteria. The gray scale indicates the number of events per bin. The rectangles enclose the signal region.

Figure 2

Proper-time distributions for (a) $K_S^0{\pi }^{+}{\pi }^{-}$ and (b) $K_S^0{K}^{+}{K}^{-}$ data in the signal region with $-2<t<4\mathrm{ps}$ (points). The curves show the fit projections for signal plus background (solid lines) and for different background components (shaded regions).

Figure 3

Central value (point) and C.L. contours (including statistical, systematic, and amplitude model uncertainties) in the $x\mathrm{\text{−}}y$ plane for $\mathrm{C}.\mathrm{L}.=68.3\%$, 95.4%, 99.7%. The no-mixing point is shown as a plus sign ($+$).