Evidence for direct CP violation from Dalitz-plot analysis of B±→K±π∓π±

We report a Dalitz-plot analysis of the charmless hadronic decays of charged B mesons to the final state K±π∓π±. Using a sample of (383.2±4.2)×106 BB̅ pairs collected by the BABAR detector, we measure CP-averaged branching fractions and direct CP asymmetries for intermediate resonant and nonresonant contributions. We find evidence for direct CP violation in the decay B±→ρ0(770)K±, with a CP-violation parameter ACP=(+44±10±4-13+5)%.