We present results for a time-dependent Dalitz plot measurement of CP-violating asymmetries in the mode B0→π+π -π0. The data set is derived from the complete sample of 471×106 BB̄ meson pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at the SLAC National Accelerator Laboratory operating on the Υ(4S) resonance. We extract parameters describing the time-dependent B0→ρπ decay probabilities and CP asymmetries, including C=0.016±0.059±0.036, ΔC=0.234±0.061±0.048, S=0.053±0.081±0.034, and ΔS=0.054±0.082±0.039, where the uncertainties are statistical and systematic, respectively. We perform a two-dimensional likelihood scan of the direct CP-violation asymmetry parameters for B0→ρ±πâ̂ decays, finding the change in χ2 between the minimum and the origin (corresponding to no direct CP violation) to be Δχ2=6.42. We present information on the CP-violating parameter α in a likelihood scan that incorporates B ±→ρπ measurements. To aid in the interpretation of our results, statistical robustness studies are performed to assess the reliability with which the true values of the physics parameters can be extracted. Significantly, these studies indicate that α cannot be reliably extracted with our current sample size, though the other physics parameters are robustly extracted. © 2013 American Physical Society.
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