Study of $B^0 \to \pi^0 \pi^0$, $B^\pm \to \pi^\pm \pi^0$, and $B^\pm \to K^\pm \pi^0$ Decays, and Isospin Analysis of $B \to \pi \pi$ Decays

We present updated measurements of the branching fractions and CP asymmetries for B0→π0π0, B±→π±π0, and B±→K±π0. Based on a sample of 383×10 6 Υ(4S)→B¯¯¯B decays collected by the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC, we measure B(B0→π0π0)=(1.47±0.25±0.12)×10−6, B(B±→π±π0)=(5.02±0.46±0.29)×10−6, and B(B±→K±π0)=(13.6±0.6±0.7)×10−6. We also measure the CP asymmetries Cπ0π0=−0.49±0.35±0.05, Aπ±π0=0.03±0.08±0.01, and AK±π0=0.030±0.039±0.010. Finally, we present bounds on the Cabibbo-Kobayashi-Maskawa angle α using isospin relations.