Measurements of neutral $B$ decay branching fractions to $K_S^0{\pi }^{+}{\pi }^{-}$ final states and the charge asymmetry of $B^0\to K^{*+}{\pi }^{-}$

We analyze the decay $B^0\to K_S^0{\pi }^{+}{\pi }^{-}$ using a sample of $232\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ factory. A maximum likelihood fit finds the following branching fractions: $\mathcal{B}(B^0\to K^0{\pi }^{+}{\pi }^{-})=(43.0\pm 2.3\pm 2.3)\times {10}^{-6},\mathcal{B}(B^0\to f_0(\to {\pi }^{+}{\pi }^{-})K^0)=(5.5\pm 0.7\pm 0.5\pm 0.3)\times {10}^{-6}$ and $\mathcal{B}(B^0\to K^{*+}{\pi }^{-})=(11.0\pm 1.5\pm 0.5\pm 0.5)\times {10}^{-6}$. For these results, the first uncertainty is statistical, the second is systematic, and the third (if present) is due to the effect of interference from other resonances. We also measure the $CP$-violating charge asymmetry in the decay $B^0\to K^{*+}{\pi }^{-}$, ${\mathcal{A}}_{K^{*}\pi }=-0.11\pm 0.14\pm 0.05$.

Figure 1

Plots of the maximum likelihood fit to data for $B^0\to K^0{\pi }^{+}{\pi }^{-}$ candidates. Plots (a)–(c) show the distributions of all events that pass the selection criteria for (a) $m_{\mathrm{ES}}$ (b) $\Delta E$ and (c) Fisher, with the solid (blue) line indicating the total model, the (red) dotted line indicating shape of the continuum background model and the (black) dashed line indicating the signal model. Plots (d)–(f) show the signal distributions for (d) $m_{ES}$, (e) $\Delta E$ and (f) Fisher, where the (black) circles are the signal distribution [17] and the solid (blue) curve is the signal PDF that was fitted in the maximum likelihood fit.

Figure 2

Maximum likelihood fits for signal distributions. For $B^0\to K^{*+}$${\pi }^{-}$ the plots show (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, and (c) the Fisher discriminant. The (black) circles are the signal distribution extracted from the data with the method of Ref. [17] and the solid curve is the signal PDF that resulted from the maximum likelihood fit. For $B^0\to f_0{K}^0$, plots show the distributions for (d) $m_{\mathrm{ES}}$, (e $\Delta E$, and (f) the Fisher discriminant, in an analogous fashion.

Figure 3

(a) shows the $m_{K_S^0\pi }$ signal distribution of $B^0\to K^0{\pi }^{+}{\pi }^{-}$ candidates [17]. The one-dimensional distribution is obtained by merging $m_{K{\pi }^{+}}^2$ and $m_{K{\pi }^{-}}^2$ into one ($m_{K\pi }^2$) by folding the Dalitz plane along the line corresponding to $m_{K{\pi }^{+}}^2=m_{K{\pi }^{-}}^2$ in order to obtain the above $m_{K\pi }$ mass distribution. (b) shows the $m_{{\pi }^{+}{\pi }^{-}}$ signal distribution of $B^0\to K^0{\pi }^{+}{\pi }^{-}$ candidates [17]. The dashed lines indicate the expected mass of the labeled resonances.

Figure 4

Distribution of the efficiency corrected cosine of the helicity angle, ${\theta }_H$, for $B^0\to K^{*\pm }{\pi }^{\mp }$ signal events.