Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>asymmetries and branching fractions in charmless two-body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-meson decays to pions and kaons

We present improved measurements of $CP$-violation parameters in the decays ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, and of the branching fractions for ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and ${B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{0}$. The results are obtained with the full data set collected at the $\ensuremath{\Upsilon}(4S)$ resonance by the BABAR experiment at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory, corresponding to $(467\ifmmode\pm\else\textpm\fi{}5)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs. We find the $CP$-violation parameter values and branching fractions: ${S}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}=\ensuremath{-}0.68\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.03$, ${C}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}=\ensuremath{-}0.25\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.02$, ${\mathcal{A}}_{{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}}=\ensuremath{-}0.107\ifmmode\pm\else\textpm\fi{}{0.016}_{\ensuremath{-}0.004}^{+0.006}$, ${C}_{{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}}=\ensuremath{-}0.43\ifmmode\pm\else\textpm\fi{}0.26\ifmmode\pm\else\textpm\fi{}0.05$, $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0})=(1.83\ifmmode\pm\else\textpm\fi{}0.21\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $\text{ }\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{0})=\phantom{\rule{0ex}{0ex}}(10.1\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, 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 ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and 6.1 standard deviations for ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, including systematic uncertainties. Constraints on the unitarity triangle angle $\ensuremath{\alpha}$ are determined from the isospin relations among the $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ rates and asymmetries. Considering only the solution preferred by the Standard Model, we find $\ensuremath{\alpha}$ to be in the range [71\ifmmode^\circ\else\textdegree\fi{},109\ifmmode^\circ\else\textdegree\fi{}] at the 68% confidence level.

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