Measurements of neutral $B$ decay branching fractions to $K_S^0{\pi }^{+}{\pi }^{-}$ final states

Branching fraction measurements using $B$-meson decays to $K_S^0{\pi }^{+}{\pi }^{-}$ are presented. These measurements were obtained by analyzing a data sample of $88.9\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ factory. Using a maximum likelihood fit, the following branching fraction results were obtained: $\mathcal{B}(B^0\to K^0{\pi }^{+}{\pi }^{-})=(43.7\pm 3.8\pm 3.4)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^{*+}{\pi }^{-})=(12.9\pm 2.4\pm 1.4)\times {10}^{-6}$, and $\mathcal{B}\mathbf{(}{B}^0\to D^{-}(\to K_S^0{\pi }^{-}){\pi }^{+}\mathbf{)}=(42.7\pm 2.1\pm 2.2)\times {10}^{-6}$. The $CP$ violating charge asymmetry ${\mathcal{A}}_{K^{*}\pi }$ for the decay $B^0\to K^{*+}{\pi }^{-}$ was measured to be ${\mathcal{A}}_{K^{*}\pi }=0.23\pm {0.18}_{-0.06}^{+0.09}$. For all these measurements the first error is statistical and the second is systematic.

Figure 1

Maximum likelihood fit projections of $m_{\mathrm{E}\mathrm{S}}$ (a), $\Delta E$ (b), and $\mathcal{F}$ (c) to the full set of $B^0\to D^{-}(\to K_S^0{\pi }^{-}){\pi }^{+}$ candidates. The dashed lines are the fitted background PDFs while the solid continuous lines are the sums of the signal and background PDFs. The solid dots are data used in the fit.

Figure 2

Maximum likelihood fit projections of $m_{\mathrm{E}\mathrm{S}}$, $\Delta E$, and $\mathcal{F}$ for signal enhanced samples of charmless $B^0\to K^0{\pi }^{+}{\pi }^{-}$ and $B^0\to K^{*+}{\pi }^{-}$ candidates. The dashed lines are the fitted background PDFs while the solid continuous lines are the sums of the signal and background PDFs. The solid dots are data. (a)–(c) have the $B^0\to K^0{\pi }^{+}{\pi }^{-}$ projections and the (d)–(f) have the $B^0\to K^{*+}{\pi }^{-}$ projections, the top, middle, and bottom rows being the $m_{\mathrm{E}\mathrm{S}}$, $\Delta E$, and $\mathcal{F}$ distributions, respectively.

Figure 3

The $m_{K\pi }$ distribution of $B^0\to K^0{\pi }^{+}{\pi }^{-}$ candidates, weighted by $\mathcal{W}$ such that background events are subtracted. The one-dimensional distribution is obtained by considering events on a Dalitz plane with axes $m_{K_S^0\pi +}^2$ and $m_{K_S^0\pi -}^2$. The two axes are merged into one ($m_{K\pi }^2$) by folding the Dalitz plane along the line corresponding to $m_{K_S^0\pi +}^2=m_{K_S^0\pi -}^2$ in order to obtain the above $m_{K\pi }$ mass distribution.