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

TL;DR

This paper extends the perturbative QCD framework with Glauber gluons to analyze B meson decays, successfully resolving the longstanding B → Kπ puzzle by matching experimental data on branching ratios and CP asymmetries.

Contribution

It introduces a unified approach incorporating Glauber gluons into QCD calculations for B decays, explaining the observed CP asymmetry differences and resolving the B → Kπ puzzle.

Findings

Predicted CP asymmetry difference matches experimental data.

Glauber gluons significantly enhance color-suppressed amplitudes.

The approach successfully explains multiple B decay modes.

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, $\Delta A_{K\pi}\equiv A_{\rm CP}^{\rm dir}(K^\pm \pi^0)[0.021 \pm 0.016] - A_{\rm CP}^{\rm dir}(K^\pm \pi^\mp)[-0.081 \pm 0.017] = 0.102 \pm 0.023$, is consistent with the measured $\Delta A_{K\pi} = 0.119 \pm 0.022$ 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.