The charmless bottom meson decays are systematically investigated based on an approximate six quark operator effective Hamiltonian from perturbative QCD. It is shown that within this framework the naive QCD factorization method provides a simple way to evaluate the hadronic matrix elements of two body mesonic decays. The singularities caused by on mass-shell quark propagator and gluon exchanging interaction are appropriately treated. Such a simple framework allows us to make theoretical predictions for the decay amplitudes with reasonable input parameters. The resulting theoretical predictions for all the branching ratios and CP asymmetries in the charmless $B^0, B^+, B_sto pipi, pi K, KK$ decays are found to be consistent with the current experimental data except for a few decay modes. The observed large branching ratio in $Bto pi^0pi^0$ decay remains a puzzle though the predicted branching ratio may be significantly improved by considering the large vertex corrections in the effective Wilson coefficients. More precise measurements of charmless bottom meson decays, especially on CP-violations in $Bto K K$ and $B_sto pipi, pi K, KK$ decay modes, will provide a useful test and guide us to a better understanding on perturbative and nonperturbative QCD.
Using the general factorization approach, we present a detailed investigation for the branching ratios, CP asymmetries and longitudinal polarization fractions in all charmless hadronic $B to VV$ decays (except for the pure annihilation processes) within the most general two-Higgs-doublet model with spontaneous CP violation. It is seen that such a new physics model only has very small contributions to the branching ratios and longitudinal polarization fractions. However, as the model has rich CP-violating sources, it can lead to significant effects on the CP asymmetries, especially on those of penguin-dominated decay modes, which provides good signals for probing new physics beyond the SM in the future B-physics experiments.
