Observation of the Rare Decay B+ \to K+pi0pi0 and Measurement of the Quasi-two Body Contributions B+ \to K*(892)+pi0, B+ \to f0(980)K+ and B+ \to chic0K+

We report an analysis of charmless hadronic decays of charged B mesons to the final state K{sup +}{pi}{sup 0}{pi}{sup 0}, using a data sample of (470.9 {+-} 2.8) x 10{sup 6} B{bar B} events collected with the BABAR detector at the {Gamma}(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 {Beta}(B{sup +} {yields} K{sup +}{pi}{sup 0}{pi}{sup 0}) = (16.2 {+-} 1.2 {+-} 1.5) x 10{sup -6} and A{sub CP}(B{sup +} {yields} K{sup +}{pi}{sup 0}{pi}{sup 0}) = -0.06 {+-} 0.06 {+-} 0.04, where the uncertainties are statistical and systematic, respectively. Additionally, we study the contributions of the B{sup +} {yields} K{sup +}(892){sup +}{pi}{sup 0}, B{sup +} {yields} f{sub 0}(980)K{sup +}, and B{sup +} {yields} {chi}{sub c0}K{sup +} quasi-two-body decays. We report the world's best measurements of the branching fraction and CP asymmetry of the B{sup +} {yields} K{sup +}{pi}{sup 0}{pi}{sup 0} and B{sup +} {yields} K{sup +}(892){sup +}{pi}{sup 0} channels.