Soft collinear effective theory analysis ofB→Kπ,B→KK¯, andB→ππdecays

$B\to K\pi$ and related decays are studied in the heavy quark limit of QCD using the soft collinear effective theory (SCET). We focus on results that follow solely from integrating out the scale $m_b$, without expanding the amplitudes for the physics at smaller scales such as ${\alpha }_s(\sqrt{E_{\pi }{\Lambda }_{\mathrm{QCD}}})$. The reduction in the number of hadronic parameters in SCET leads to multiple predictions without the need of SU(3). We find that the $CP$-asymmetry in $B^{-}\to {\pi }^0{K}^{-}$ should have a similar magnitude and the same sign as the well measured asymmetry in ${\overline{B}}^0\to {\pi }^{+}{K}^{-}$. Our prediction for $\mathrm{Br}(K^{+}{\pi }^{-})$ exceeds the current experimental value at the $2\sigma$ level. We also use our results to determine the corrections to the Lipkin and $CP$-asymmetry sum rules in the standard model and find them to be quite small, thus sharpening their utility as a tool to look for new physics.