Measurement of CP-Violating Asymmetries in B⁰ → (ρπ)⁰ Decays Using a Time-Dependent Dalitz Plot Analysis

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 x 10⁶ BB̅ 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 → ρπθ decay probabilities and CPθ 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^± π^∓ decays, finding the change in χ² between the minimum and the origin (corresponding to no direct CPθ violation) to be Δχ² = 6.42. We present information on the CP-violating parameter αθ in a likelihood scan that incorporates B^± → ρπθ 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 αθ cannot be reliably extracted with our current sample size, though the other physics parameters are robustly extracted.