Measurement of $D^0\mathrm{\text{−}}{\overline{D}}^0$ Mixing from a Time-Dependent Amplitude Analysis of $D^0\to K^{+}{\pi }^{-}{\pi }^0$ Decays

We present evidence of $D^0\mathrm{\text{−}}{\overline{D}}^0$ mixing using a time-dependent amplitude analysis of the decay $D^0\to K^{+}{\pi }^{-}{\pi }^0$ in a data sample of $384{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ collider at the Stanford Linear Accelerator Center. Assuming $CP$ conservation, we measure the mixing parameters $x_{K\pi {\pi }^0}^{\prime }=[{2.61}_{-0.68}^{+0.57}(\mathrm{stat})\pm 0.39(\mathrm{syst})]\%$, $y_{K\pi {\pi }^0}^{\prime }=[-{0.06}_{-0.64}^{+0.55}(\mathrm{stat})\pm 0.34(\mathrm{syst})]\%$. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of $CP$ violation in mixing.

Figure 1

Dalitz plots for the (a) RS and (b) WS $D^0$ samples. The reconstructed (c) $D^0$ mass and (d) $\Delta m$ distributions for the WS sample requiring, respectively, (c) $0.1449<\Delta m<0.1459\mathrm{GeV}/c^2$ and (d) $1.8495<m_{K\pi {\pi }^0}<1.8795\mathrm{GeV}/c^2$. The fit results are shown by the superimposed curves. The light histogram represents the mistag background, while the dark histogram shows the combinatorial background.

Figure 2

(a) Proper time distribution for RS events with the fit result superimposed. The distribution of background events is shown by the shaded histogram. (b) Proper time distribution for WS events. (c), (d) $m_{K^{+}{\pi }^{-}}^2$ and $m_{K^{+}{\pi }^0}^2$ projections with superimposed fit results (line). The light histogram represents the mistag background, while the dark histogram shows the combinatoric background.