Measurements of the Branching Fraction and $CP$-Violation Asymmetries in $B^0\to f_0(980)K_S^0$

We present measurements of the branching fraction and $CP$-violating asymmetries in the decay $B^0\to f_0(980)K_S^0$. The results are obtained from a data sample of $123\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays. From a time-dependent maximum likelihood fit, we measure the branching fraction $\mathcal{B}\mathbf{(}{B}^0\to f_0(980)(\to {\pi }^{+}{\pi }^{-})K^0\mathbf{)}=(6.0\pm 0.9\pm 0.6\pm 1.2)\times {10}^{-6}$, the mixing-induced $CP$ violation parameter $S=-{1.62}_{-0.51}^{+0.56}\pm 0.09\pm 0.04$, and the direct $CP$ violation parameter $C=0.27\pm 0.36\pm 0.10\pm 0.07$, where the first errors are statistical, the second systematic, and the third due to model uncertainties. We measure the $f_0(980)$ mass and width to be $m_{f_0}(980)=(980.6\pm 4.1\pm 0.5\pm 4.0)\mathrm{M}\mathrm{e}\mathrm{V}/c^2$ and ${\Gamma }_{f_0}(980)=({43}_{-9}^{+12}\pm 3\pm 9)\mathrm{M}\mathrm{e}\mathrm{V}/c^2$, respectively.

Figure 1

Distributions of (clockwise from bottom left) $\mathrm{N}\mathrm{N}$, $m({\pi }^{+}{\pi }^{-})$, $\Delta E$, $m_{\mathrm{E}\mathrm{S}}$, and $|\cos \theta ({\pi }^{+})|$ for samples enhanced in the $f_0{K}_S^0$ signal. For presentation purposes, the region $0.765<|\cos \theta ({\pi }^{+})|<0.81$ has been removed to suppress the contribution from $D^{-}{\pi }^{+}$ events. The bottom-right plot shows the distribution of the ratio of the signal likelihood to the total likelihood for all events entering the fit. In each plot, the solid curve represents a projection of the maximum likelihood fit result, the dashed curve represents the contribution from continuum events, and the dotted line indicates the combined contributions from continuum and $B$-background events.

Figure 2

The signal-enhanced time distributions tagged as $B_{\mathrm{t}\mathrm{a}\mathrm{g}}^0$ (top) and ${\overline{B}}_{\mathrm{t}\mathrm{a}\mathrm{g}}^0$ (middle), and the asymmetry, $A_{B^0/{\overline{B}}^0}$ (bottom). The solid curve is a projection of the fit result. The dashed line is the distribution for continuum background and the dotted line is the total $B$- and continuum-background contribution.