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

Abstract

We extend the perturbative QCD formalism including the Glauber gluons, which has been shown to accommodate the measured $B\to \pi \pi$ and $B^0\to {\rho }^0{\rho }^0$ branching ratios simultaneously, to the analysis of the $B\to K\pi$ 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, $\Delta A_{K\pi }\equiv A_{\mathrm{CP}}^{\mathrm{dir}}(K^{\pm }{\pi }^0)[0.021\pm 0.016]-A_{\mathrm{CP}}^{\mathrm{dir}}(K^{\pm }{\pi }^{\mp })[-0.081\pm 0.017]=0.102\pm 0.023$, is consistent with the measured $\Delta A_{K\pi }=0.119\pm 0.022$ 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.

Comments: Revtex file, 6 pages, 4 tables, and 1 figure; to appear in PRD, matching the published version