Dalitz plot analysis of the decay B0(B̄0)→K±ππ0

We report a Dalitz-plot analysis of the charmless hadronic decays of neutral B mesons to K±ππ0. With a sample of (231.8±2.6) ×106Υ(4S)→BB̄ decays collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for B0 and B̄0 decays and determine the corresponding CP-averaged branching fractions and charge asymmetries. The inclusive branching fraction and CP-violating charge asymmetry are measured to be B(B0→K+π-π0)=(35.7-1.5+2.6±2.2) ×10-6 and ACP=-0.030-0.051+0.045±0.055 where the first errors are statistical and the second systematic. We observe the decay B0→K* 0(892)π0 with the branching fraction B(B0→K*0(892)π0)=(3.6-0. 8+0.7±0.4)×10-6. This measurement differs from zero by 5.6 standard deviations (including the systematic uncertainties). The selected sample also contains B0→D̄0π0 decays where D̄0→K+π-, and we measure B(B0→D̄0π0)=(2.93±0.17±0.18)×10-4.