Improved measurements of the branching fractions for $\overrightarrow{B}K\pi ,$ ππ, and $K\overline{K}$ decays

We report improved measurements of branching fractions for $\overrightarrow{B}K\pi ,$ ${\pi }^{+}{\pi }^{-},$ ${\pi }^{+}{\pi }^0,$ and $K\overline{K}$ decays based on a data sample of 85.0 million $B\overline{B}$ pairs collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ storage ring. This data sample is almost three times larger than the sample previously used. We observe clear signals for $\overrightarrow{B}K\pi ,$ ${\pi }^{+}{\pi }^{-},$ and ${\pi }^{+}{\pi }^0$ decays and set upper limits on $\overrightarrow{B}K\overline{K}$ decays. The results can be used to give model-dependent constraints on the CKM angle ${\phi }_3,$ as well as limits on the hadronic uncertainty in the time-dependent analysis of the angle ${\phi }_2.$