Observation of the DecayB±→π±π0, Study ofB±→K±π0, and Search forB0→π0π0

We present results for the branching fractions and charge asymmetries in B+/--->h(+/-)pi(0) (where h(+/-)=pi(+/-),K+/-) and a search for the decay B0-->pi(0)pi(0) using a sample of approximately 88 x 10(6) BBmacr; pairs collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We measure B(B+/--->pi(+/-)pi(0))=(5.5(+1.0)(-0.9)+/-0.6)x10(-6), where the first error is statistical and the second is systematic. The B+/--->pi(+/-)pi(0) signal has a significance of 7.7sigma including systematic uncertainties. We simultaneously measure the K+/-pi(0) branching fraction to be B(B+/--->K+/-pi(0))=(12.8(+1.2)(-1.1)+/-1.0)x10(-6). The charge asymmetries are Api(+/-)(pi(0))=-0.0…