Resolving the $B\to K\pi$ puzzle by Glauber-gluon effects

We extend the perturbative QCD formalism including the Glauber gluons, which has been shown to accommodate the measured $B\to \pi \pi$ and $B^0\to\rho^0 \rho^0$branchingratiossimultaneously,totheanalysisofthe$B \to K \pi$and$K \bar K$ decays. It is observed that the convolution of the universal Glauber phase factors with the transverse-momentum-dependent kaon wave function reveals weaker (stronger) Glauber effects than in the pion ($\rho$ meson) case as expected. Our predictions for the branching ratios and the direct CP asymmetries of the $B\to K\pi$ and $K\bar{K}$ modes at next-to-leading-order accuracy agree well with data. In particular, the predicted difference of the $B^{\pm }\to K^{\pm }{\pi }^0$ and $B^0\to K^{\pm }{\pi }^{\mp }$ direct CP asymmetries, $\Delta A_{K\pi}\equiv A_{\rm CP}^{\rm dir}(K^\pm \pi^0)[0.021 \pm 0.016] - A_{\rm CP}^{\rm dir}(K^\pm \pi^\mp)[-0.081 \pm 0.017] = 0.102 \pm 0.023$, is consistent with the measured $\mathrm{\Delta }{A}_{K\pi }=0.119\pm 0.022$ within uncertainties, and the known $B\to K\pi$ puzzle is resolved. The above $B \to \pi \pi$,$K\pi$and$K \bar K$ studies confirm that the Glauber gluons associated with pseudo-Nambu-Goldstone bosons enhance the color-suppressed tree amplitude significantly, but have a small impact on other topological amplitudes.