Measurement of the $CP$ Asymmetry and Branching Fraction of $B^0\to {\rho }^0{K}^0$

We present a measurement of the branching fraction and time-dependent $CP$ asymmetry of $B^0\to {\rho }^0{K}^0$. The results are obtained from a data sample of $227\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at Stanford Linear Accelerator Center. From a time-dependent maximum likelihood fit yielding $111\pm 19$ signal events, we find $\mathcal{B}(B^0\to {\rho }^0{K}^0)=(4.9\pm 0.8\pm 0.9)\times {10}^{-6}$, where the first error is statistical and the second systematic. We report the measurement of the $CP$ parameters $S_{{\rho }^0{K}_S^0}=0.20\pm 0.52\pm 0.24$ and $C_{{\rho }^0{K}_S^0}=0.64\pm 0.41\pm 0.20$.

Figure 1

${}_s\mathcal{P}lots$ of maximum likelihood fit discriminating variables: (a) $m_{\mathrm{ES}}$, (b) $\Delta E$, (c) neural network output, (d) $\cos {\theta }_{{\pi }^{+}}$, and (e) invariant mass of the ${\pi }^{+}{\pi }^{-}$ combination. Lines are projections of signal PDFs for each variable. (f) is a plot of the likelihood of an event being signal calculated for all events in our data set and compared to the predictions of our PDF (predicted continuum in light gray, $B$ background in dark gray, and signal unshaded).

Figure 2

${}_s\mathcal{P}lots$ of $\Delta t$, overlaid with projected signal PDFs, split into (a) $B_{\mathrm{tag}}^0$ tags, (b) ${\overline{B}}_{\mathrm{tag}}^0$ tags, and (c) the asymmetry $(N_{B^0\mathrm{tag}}-N_{{\overline{B}}^0\mathrm{tag}})/(N_{B^0\mathrm{tag}}+N_{{\overline{B}}^0\mathrm{tag}})$ as a function of $\Delta t$.