Charmless $B\to PP, PV, VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects

TL;DR

This paper presents a systematic QCD-based analysis of charmless B meson decays into pseudoscalar and vector mesons, incorporating strong phase effects and power corrections to predict branching ratios, CP asymmetries, and polarization observables.

Contribution

It introduces a six-quark operator effective Hamiltonian approach with strong phase effects, providing predictions consistent with experimental data for various B decay modes.

Findings

Predicted branching ratios align with current measurements.

Analyzed the impact of annihilation amplitudes with strong phases.

Provided detailed predictions for polarization fractions in VV decays.

Abstract

Based on an approximate six-quark operator effective Hamiltonian from perturbative QCD, we present a systematical study of charmless $B \to PP, PV, VV$ decays ($P$ and $V$ denoting pseudoscalar and vector mesons, respectively). The calculation of the relevant hard-scattering kernels is completed, the resulting transition form factors are consistent with the results of QCD sum rule calculation. Important classes of power corrections include "chirally-enhanced" terms, vertex corrections and weak annihilation contributions with non-trivial strong phase. With these considerations, predictions are presented for the branching ratios and CP asymmetries of B-meson decays into PP, PV and VV final states, and also for the corresponding polarization observables in VV final states. Several decay modes and observables, which are of particular interest phenomenologically, are discussed in detail, including the effect of annihilation amplitude with strong phase, the $\pi\pi$, $\pi K$ and $\pi \rho$ systems, the longitudinal polarization fraction $f_L$ in $\rho K^*$ and $\phi K^*$ systems and so on. It is observed that predictions in our framework generally agree with the current experimental data.