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

Abstract

We extend the perturbative QCD formalism including the Glauber gluons, which has been shown to accommodate the measured $B \to ππ$ and $B^0\toρ^0 ρ^0$ branching ratios simultaneously, to the analysis of the $B \to K π$ 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 ($ρ$ meson) case as expected. Our predictions for the branching ratios and the direct CP asymmetries of the $B \to K π$ and $K \bar K$ modes at next-to-leading-order accuracy agree well with data. In particular, the predicted difference of the $B^\pm \to K^\pm π^0$ and $B^0 \to K^\pm π^\mp$ direct CP asymmetries, $ΔA_{Kπ}\equiv A_{\rm CP}^{\rm dir}(K^\pm π^0)[0.021 \pm 0.016] - A_{\rm CP}^{\rm dir}(K^\pm π^\mp)[-0.081 \pm 0.017] = 0.102 \pm 0.023$, is consistent with the measured $ΔA_{Kπ} = 0.119 \pm 0.022$ within uncertainties, and the known $B \to Kπ$ puzzle is resolved. The above $B \to ππ$, $Kπ$ 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.