Dalitz plot analysis of B±→π±π±π∓ decays

We present a Dalitz plot analysis of charmless B± decays to the final state π±π±π∓ using a sample of (465±5)×106 BB̅ pairs collected by the BABAR experiment at √s=10.58  GeV. We measure the branching fractions B(B±→π±π±π∓)=(15.2±0.6±1.2±0.4)×10-6, B(B±→ρ0(770)π±)=(8.1±0.7±1.2-1.1+0.4)×10-6, B(B±→f2(1270)π±)=(1.57±0.42±0.16-0.19+0.53)×10-6, and B(B±→π±π±π∓ nonresonant)=(5.3±0.7±0.6-0.5+1.1)×10-6, where the uncertainties are statistical, systematic, and model-dependent, respectively. Measurements of branching fractions for the modes B±→ρ0(1450)π± and B±→f0(1370)π± are also presented. We observe no significant direct CP asymmetries for the above modes, and there is no evidence for the decays B±→f0(980)π±, B±→χc0π±, or B±→χc2π±.