We present measurements of branching fractions and $CP$-violating asymmetries in $B^0\to {\rho }^{\pm }{\pi }^{\mp }$ and $B^0\to {\rho }^{-}{K}^{+}$ decays. The results are obtained from 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. From a time-dependent maximum likelihood fit we measure the branching fractions $\mathcal{B}(B^0\to {\rho }^{\pm }{\pi }^{\mp })=[22.6\pm 1.8\mathrm{(}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{)}\pm 2.2\mathrm{(}\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{)}]\times {10}^{-6}$ and $\mathcal{B}(B^0\to {\rho }^{-}{K}^{+})=({7.3}_{-1.2}^{+1.3}\pm 1.3)\times {10}^{-6}$, and the $CP$-violating charge asymmetries $A_{CP}^{\rho \pi }=-0.18\pm 0.08\pm 0.03$ and $A_{CP}^{\rho K}=0.28\pm 0.17\pm 0.08$, the direct $CP$ violation parameter $C_{\rho \pi }=0.36\pm 0.18\pm 0.04$ and the mixing-induced $CP$ violation parameter $S_{\rho \pi }=0.19\pm 0.24\pm 0.03$, and the dilution parameters $\Delta C_{\rho \pi }={0.28}_{-0.19}^{+0.18}\pm 0.04$ and $\Delta S_{\rho \pi }=0.15\pm 0.25\pm 0.03$.

• Received 13 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.201802