Measurement of CP-Violating Asymmetries in $B^0\to(\rho\pi)^0$ Using a Time-Dependent Dalitz Plot Analysis

We report a measurement of CP-violating asymmetries in $B^0\to(\rho\pi)^0\to\pi^+\pi^-\pi^0$ decays using a time-dependent Dalitz plot analysis. The results are obtained from a data sample of 347 million $\Upsilon(4S) \to B\bar{B}$ decays, collected by the BaBar detector at the PEP-II asymmetric-energy B Factory at SLAC. We measure 26 coefficients of the bilinear form factor terms occurring in the time-dependent decay rate of the \Bz meson and derive the physically relevant quantities from these coefficients. In particular we find a three standard deviation evidence of direct CP-violation in $B^0\to\rho^\pm\pi^\mp$ decays, with systematic uncertainties included. We also achieve a constraint of the angle $\alpha$ of the Unitarity Triangle. All results presented are preliminary.