First Measurement of the <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mn>0</mn></msup><msup><mi>π</mi><mn>0</mn></msup></math> Branching Fraction and <math><mrow><mi>C</mi><mi>P</mi></mrow></math> Asymmetry

We study B+→π+π0π0 using 711 fb−1 of data collected at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e− collider. We measure an inclusive branching fraction of (19.0&#177;1.5&#177;1.4)&#215;10−6 and an inclusive CP asymmetry of (9.2&#177;6.8&#177;0.7)%, where the first uncertainties are statistical and the second are systematic, and a B+→ρ(770)+π0 branching fraction of (11.2&#177;1.1&#177;0.9−1.6+0.8)&#215;10−6, where the third uncertainty is due to possible interference with B+→ρ(1450)+π0. We present the first observation of a structure around 1 GeV/c2 in the π0π0 mass spectrum, with a significance of 6.4σ, and measure a branching fraction to be (6.9&#177;0.9&#177;0.6)&#215;10−6. We also report a measurement of local CP asymmetry in this structure.