Branching Fractions and Direct CP Violation in Charmless Three-body Decays of B Mesons

TL;DR

This paper models charmless three-body B meson decays to analyze CP violation, finding good agreement with some experimental results and proposing rescattering effects as a solution to CP asymmetry sign discrepancies.

Contribution

It introduces a factorization-based model for three-body B decays, incorporating resonant and nonresonant contributions, and addresses CP violation sign puzzles with rescattering effects.

Findings

Good agreement with experimental CP violation in some decay modes.

Incorrect sign predictions for certain CP asymmetries without rescattering.

Rescattering effects can correct CP asymmetry signs.

Abstract

Charmless three-body decays of B mesons is studied using a simple model based on the framework of the factorization approach. Hadronic three-body decays receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated three-body decays arise from the $b\to u$ tree transition which can be evaluated using heavy meson chiral perturbation theory valid in the soft meson limit. For penguin-dominated decays, nonresonant signals come mainly from the penguin amplitude governed by the matrix elements of scalar densities $<M_1M_2|\bar q_1 q_2|0>$. We use the measurements of $\bar B^0\to K_SK_SK_S$ to constrain the nonresonant component of $<K\bar K|\bar ss|0>$. The intermediate vector meson contributions to three-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. While the calculated direct CP violation in $B^-\to K^+K^-K^-$ and $B^-\to \pi^+\pi^-\pi^-$ decays agrees well with experiment in both magnitude and sign, the predicted CP asymmetries in $B^-\to \pi^- K^+K^-$ and $B^-\to K^-\pi^+\pi^-$ are wrong in signs when confronted with experiment. It has been conjectured recently that a possible resolution to this CP puzzle may rely on final-state rescattering of $\pi^+\pi^-$ and $K^+K^-$. Assuming a large strong phase associated with the matrix element $<K\pi|\bar sq|0>$ arising from some sort of power corrections, we fit it to the data of $K^-\pi^+\pi^-$ and find a correct sign for $\pi^- K^+K^-$.