Observation of the rare decay B+→K+π0π0 and measurement of the quasi-two-body contributions B+→K* (892)+π0, B+→f0(980)K+, and B+→χc0K+

We report an analysis of charmless hadronic decays of charged B mesons to the final state K+π0π0, using a data sample of (470.9±2.8)×106 BB̄ events collected with the BABAR detector at the Υ(4S) resonance. We observe an excess of signal events, with a significance above 10 standard deviations including systematic uncertainties, and measure the branching fraction and CP asymmetry to be B(B +→K+π0π0)=(16.2±1.2±1.5) ×10-6 and ACP(B+→K +π0π0)=-0.06±0.06±0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B+→K*(892) +π0, B+→f0(980)K+, and B+→χc0K+ quasi-two-body decays. We report the world's best measurements of the branching fraction and CP asymmetry of the B+→K+π0π0 and B+→K *(892)+π0 channels.