Observation of the rare decay B[superscript +]→K[superscript +]π[superscript 0]π[superscript 0] and measurement of the quasi-two-body contributions B[superscript +]→K*(892)[superscript +]π[superscript 0], B[superscript +]→f[subscript 0](980)K[superscript +], and B[superscript +]→χ[subscript c0]K[superscript +]

We report an analysis of charmless hadronic decays of charged B mesons to the final state K[superscript +]π[superscript 0]π[superscript 0], using a data sample of (470.9±2.8)×10[superscript 6] BB̅ 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[superscript +]→K[superscript +]π[superscript 0]π[superscript 0])=(16.2±1.2±1.5)×10[superscript -6] and A[subscript CP](B[superscript +]→K[superscript +]π[superscript 0]π[superscript 0])=-0.06±0.06±0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B[superscript +]→K*(892)[superscript +]π[superscript 0], B[superscript +]→f[superscript 0](980)K[superscript +], and B[superscript +]→χ[subscript c0]K[superscript +] quasi-two-body decays. We report the world’s best measurements of the branching fraction and CP asymmetry of the B[superscript +]→K[superscript +]π[superscript 0]π[superscript 0] and B[superscript +]→K*(892)[superscript +]π[superscript 0] channels