Measurement of theCPAsymmetry and Branching Fraction ofB0→ρ0K0

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 $C_{{\rho }^0{K}_S^0}=0.64\pm 0.41\pm 0.20$.