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Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons

We present improved measurements of CP-violation parameters in the decays $B^0 \to π^+ π^-$, $B^0 \to K^+ π^-$, and $B^0 \to π^0 π^0$, and of the branching fractions for $B^0 \to π^0 π^0$ and $B^0 \to K^0 π^0$. The results are obtained with the full data set collected at the $Υ(4S)$ resonance by the BABAR experiment at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory, corresponding to $467 \pm 5$ million $B\bar B$ pairs. We find the CP-violation parameter values and branching fractions $ S_{π^+π^-} = -0.68 \pm 0.10 \pm 0.03, C_{π^+π^-} = -0.25 \pm 0.08 \pm 0.02, A_{K^-π^+} = -0.107 \pm 0.016 ^{+0.006}_{-0.004}, C_{π^0π^0} = -0.43 \pm 0.26 \pm 0.05, Br(B^0 \to π^0 π^0) = (1.83 \pm 0.21 \pm 0.13) \times 10^{-6}, Br(B^0 \to K^0 π^0) = (10.1 \pm 0.6 \pm 0.4) \times 10^{-6},$ where in each case, the first uncertainties are statistical and the second are systematic. We observe CP violation with a significance of 6.7 standard deviations for $B^0 \toπ^+π^-$ and 6.1 standard deviations for $B^0 \to K^+ π^-$, including systematic uncertainties. Constraints on the Unitarity Triangle angle $α$ are determined from the isospin relations among the $B \to ππ$ rates and asymmetries. Considering only the solution preferred by the Standard Model, we find $α$ to be in the range $[71^\circ,109^\circ]$ at the 68% confidence level.