We present a time-dependent analysis of $CP$ violation in $B^0\to {\rho }^{\pm }{\pi }^{\mp }$ decays based on a $140{\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}(4S)$ resonance with the Belle detector at KEKB. We obtain the charge asymmetry ${\mathcal{A}}_{CP}^{\rho \pi }=-0.16\pm 0.10(\mathrm{stat})\pm 0.02(\mathrm{syst})$. An unbinned maximum-likelihood fit to the $\Delta t$ distributions yields $C_{\rho \pi }=0.25\pm 0.17(\mathrm{stat}{)}_{-0.06}^{+0.02}(\mathrm{syst})$, $\Delta C_{\rho \pi }=0.38\pm 0.18(\mathrm{stat}{)}_{-0.04}^{+0.02}(\mathrm{syst})$, $S_{\rho \pi }=-0.28\pm 0.23(\mathrm{stat}{)}_{-0.08}^{+0.10}(\mathrm{syst})$, and $\Delta S_{\rho \pi }=-0.30\pm 0.24(\mathrm{stat})\pm 0.09(\mathrm{syst})$. The direct $CP$ violation parameters for $B\to {\rho }^{+}{\pi }^{-}$ and $B\to {\rho }^{-}{\pi }^{+}$ decays are ${\mathcal{A}}_{\rho \pi }^{+-}=-0.02\pm 0.16(\mathrm{stat}{)}_{-0.02}^{+0.05}(\mathrm{syst})$ and ${\mathcal{A}}_{\rho \pi }^{-+}=-0.53\pm 0.29(\mathrm{stat}{)}_{-0.04}^{+0.09}(\mathrm{syst})$.

• Received 1 August 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.121801