Search for $CP$ violation in $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$

We report on a search for $CP$ violation in the decay of $D^0$ and ${\overline{D}}^0$ to $K_S^0{\pi }^{+}{\pi }^{-}$. The data come from an integrated luminosity of $9.0{\mathrm{f}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collisions at $\sqrt{s}\approx 10\mathrm{G}\mathrm{e}\mathrm{V}$ recorded with the CLEO II.V detector. The resonance substructure of this decay is well described by ten quasi-two-body decay channels plus a small nonresonant component. We observe no evidence for $CP$ violation in the amplitudes that describe the decay $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$.

Figure 1

Distribution of $Q$ (a),(b) and $M$ (c),(d) for the process $D^0$ and ${\overline{D}}^0\to K_S^0{\pi }^{+}{\pi }^{-}$. The candidates pass all selection criteria discussed in the text.

Figure 2

Dalitz distribution for (a) $D^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and (b) ${\overline{D}}^0\to K_S^0{\pi }^{+}{\pi }^{-}$ candidates passing all selection criteria discussed in Ref. [17]. The horizontal axis $(m_{RS}{)}^2$ corresponds to $(m_{K_S^0{\pi }^{-}}{)}^2$ for $D^0$ and $(m_{K_S^0{\pi }^{+}}{)}^2$ for ${\overline{D}}^0$.

Figure 3

Projections of the results of the fit described in the text to the $K_S^0{\pi }^{+}{\pi }^{-}$ Dalitz distribution showing both the fit (histogram) and the data (points). The combined $D^0$ and ${\overline{D}}^0$ samples are shown in (a)–(c). The difference between the $D^0$ and ${\overline{D}}^0$ samples is shown in (d)–(f).