Study of B0 -> pi0 pi0, B -> pi pi0, and B -> K pi0 Decays, and Isospin Analysis of B -> pipi Decays

We present updated measurements of the branching fractions and CP asymmetries for B0 -> pi0 pi0, B+ -> pi+ pi0, and B+ -> K+ pi0. Based on a sample of 383 x 10^6 Upsilon(4S) -> B Bbar decays collected by the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC, we measure B(B0 -> pi0 pi0) =(1.47 +/- 0.25 +/- 0.12) x 10^-6, B(B+ -> pi+ pi0)= (5.02 +/- 0.46 +/- 0.29) x 10^-6, and B(B+ -> K+ pi0) = (13.6 +/- 0.6 +/- 0.7) x 10^-6. We also measure the CP asymmetries C(pi0 pi0) = -0.49 +/- 0.35 +/- 0.05, A(pi+ pi0) = 0.03 +/- 0.08 +/- 0.01, and A(K+ pi0) = 0.030 +/- 0.039 +/- 0.010. Finally, we present bounds on the CKM angle $\alpha$ using isospin relations.