$B\to K\pi$ decays

Though QCD Factorization(QCDF) could produce sufficiently large $B\to K\pi$ branching ratios close to experiments, the predicted direct CP asymmetry in ${\bar B}^{0}\to K^{+}\pi^{-}$ decay is however still quite below experiment, even with a large negative phase in the annihilation term, according to existing calculations. This suggests the presence of an additional strong phase in the decay amplitude which could come from the long-distance final state interactions(FSI) like charming penguin. In this paper, we show that, by adding to the $B\to K\pi$ decay QCDF amplitude, a real part and an absorptive part with a strength 10% and 30% of the penguin amplitude, respectively, we could bring the $B\to K\pi$ branching ratios and the ${\bar B}^{0}\to K^{-}\pi^{+}$ CP asymmetry close to the measured values. We also find that the color-allowed electroweak penguin is appreciable and that from the QCDF electroweak-strong penguin interference terms and the measured $B^{-}\to {\bar K}^{0}\pi^{-}$ we obtain $(9.0\pm 0.3)\times 10^{-6}$ for the ${\bar B}^{0}\to {\bar K}^{0}\pi^{0}$ branching ratio, a bit lower than experiment. Similarly, the predicted value for $B^{-}\to K^{-}\pi^{0}$ in terms of the ${\bar B}^{0}\to K^{-}\pi^{+}$ branching ratio agrees well with experiment. This suggests that the measured value for ${\bar B}^{0}\to {\bar K}^{0}\pi^{0}$ in fact should be lower than the current measured value.