Measurement of CP Asymmetries and Branching Fractions in a Time-Dependent Dalitz Analysis of B^0-->(rho pi)^0 and a Constraint on the Quark Mixing Angle phi_2

We present the results of a time-dependent Dalitz plot analysis of B0 --> pi+ pi- pi0 decays based on a 414/fb data sample that contains 449 x 10^6 BB pairs. The data was collected on the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e+e- collider. Combining our analysis with information on charged B decay modes, we perform a full Dalitz and isospin analysis and obtain a constraint on the quark mixing angle phi_2, 68deg. < phi_2 < 95deg. at the 68.3% confidence level for the phi_2 solution consistent with the standard model (SM). A large SM-disfavored region also remains. The branching fractions for the decay processes of B0 --> rho+-(770) pi-+ and B0 --> rho0(770) pi0 are measured to be (22.6 +- 1.1[stat.] +- 4.4 [syst.]) x 10^{-6} and (3.0 +- 0.5 [stat.] +- 0.7 [syst.]) x 10^{-6}, respectively. These are the first branching fraction measurements of the process B0 --> rho(770)pi with the lowest resonance rho(770) explicitly separated from the radial excitations.