Measurements of B⁰ decays to pi^+pi^-pi⁰

We present preliminary results of searches for exclusive $B^0$ decays to $\pi^+\pi^-\pi^0$ among 22.7 million $b\bar{b}$ pairs collected by the BABAR experiment from electron-positron collisions near the $\Upsilon(4S)$ resonance. We measure $\cal{B}(\rho^\mp \pi^\pm) = (28.9\pm 5.4\pm 4.3)\times 10^{-6}$, and find no evidence for the presence of any other decay mode in the $\pi^+\pi^-\pi^0$ Dalitz plot. Upper limits are determined for the branching fractions of $B^0\to\rho^0\pi^0$, non-resonant $B^0$ decays to $\pi^+\pi^-\pi^0$ and of several discrete regions of $\pi^+\pi^-\pi^0$ phase-space. We also measure the direct CP-violating asymmetry between the rates of untagged $\rho^+\pi^-$ and $\rho^-\pi^+$, finding no significant evidence for an effect.