Time-dependent Dalitz plot measurement of $CP$ parameters in $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decays

We present a time-dependent Dalitz plot measurement of $CP$ violation parameters in $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$ decays. These results are obtained from a large data sample that contains $657\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. For the $CP$ violation parameters, we obtain two consistent solutions that describe the data well. The first of these solutions may be preferred by external information from other measurements. There is no evidence for direct $CP$ violation in $B^0\to {\rho }^0(770)K_S^0$, $B^0\to f_0(980)K_S^0$ and $B^0\to K^{*+}(892){\pi }^{-}$, while measurements of mixing-induced $CP$ violation in $B^0\to {\rho }^0(770)K_S^0$ and $B^0\to f_0(980)K_S^0$ decays are consistent with that of $b\to c\overline{c}s$ decays. We also measured the phase difference between $B^0\to K^{*+}(892){\pi }^{-}$ and ${\overline{B}}^0\to K^{*-}(892){\pi }^{+}$, which may be used to extract ${\varphi }_3$.

Figure 1

Fit result for $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$ signal yield. The solid curve shows the fit result, the dotted curve represents $B\overline{B}$ and the dashed curve is the sum of the $q\overline{q}$ and $B\overline{B}$ components.

Figure 2

Signal enhanced Dalitz plot fit for $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$. When plotting a two-particle mass projection, we require the invariant mass of the other two two-particle combinations to be greater than $1.5\mathrm{GeV}/c^2$. The solid curve shows the fit result while the shaded and dashed curves show the $q\overline{q}$ and total background components, respectively.

Figure 3

Time-dependent Dalitz plot fit results for $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$ in (a), the ${\rho }^0(770)$ region and (b), the $f_0(980)$ region using Solution 1. The top plots show the $\Delta t$ distribution for $B^0$ and ${\overline{B}}^0$ tags indicated by the solid and dashed curves, respectively. These plots contain only good tags, $0.5<r\le 1.0$ and the dotted curve represents the background contribution. The bottom plots show the $B^0{\overline{B}}^0$ raw asymmetry of the top plots, $(N_{B^0}-N_{{\overline{B}}^0})/(N_{B^0}+N_{{\overline{B}}^0})$, where $N_{B^0}(N_{{\overline{B}}^0})$ is the number of $B^0$ (${\overline{B}}^0$) tags in $\Delta t$.

Figure 4

Statistical likelihood scan of ${\varphi }_1^{\mathrm{eff}}$ for $B^0\to {\rho }^0(770)K_S^0$ (a), and $B^0\to f_0(980)K_S^0$ (b) where the solid (dashed) curve represents Solution 1 (2).

Figure 5

Likelihood scans of ${\varphi }_1^{\mathrm{eff}}$ for $B^0\to {\rho }^0(770)K_S^0$ (top) and $B^0\to f_0(980)K_S^0$ (bottom) for Solution 1 (left) and Solution 2 (right). The solid (dashed) curve contains the total (statistical) error and the dotted box indicates the parameter range corresponding to $\pm 1\sigma$.

Figure 6

Likelihood scans of ${\mathcal{S}}_{CP}^{\mathrm{eff}}$ for $B^0\to {\rho }^0(770)K_S^0$ (top) and $B^0\to f_0(980)K_S^0$ (bottom) for Solution 1 (left) and Solution 2 (right). The solid (dashed) curve contains the total (statistical) error and the dotted box indicates the parameter range corresponding to $\pm 1\sigma$. The statistical error of ${\mathcal{S}}_{CP}^{\mathrm{eff}}$ is determined from these scans.

Figure 7

Likelihood scan of $\Delta \varphi$ for Solution 1 (left) and Solution 2 (right). The solid (dashed) curve contains the total (statistical) error and the dotted box indicates the parameter range corresponding to $\pm 1\sigma$.