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The charmless bottom meson decays are systematically investigated based on anapproximate six quark operator effective Hamiltonian from perturbative QCD. Itis shown that within this framework the naive QCD factorization method providesa simple way to evaluate the hadronic matrix elements of two body mesonicdecays. The singularities caused by on mass-shell quark propagator and gluonexchanging interaction are appropriately treated. Such a simple frameworkallows us to make theoretical predictions for the decay amplitudes withreasonable input parameters. The resulting theoretical predictions for all thebranching ratios and CP asymmetries in the charmless $B^0, B^+, B_s\to \pi\pi,\pi K, KK$ decays are found to be consistent with the current experimental dataexcept for a few decay modes. The observed large branching ratio in $B\to\pi^0\pi^0$ decay remains a puzzle though the predicted branching ratio may besignificantly improved by considering the large vertex corrections in theeffective Wilson coefficients. More precise measurements of charmless bottommeson decays, especially on CP-violations in $B\to K K$ and $B_s\to \pi\pi, \piK, KK$ decay modes, will provide a useful test and guide us to a betterunderstanding on perturbative and nonperturbative QCD.

international journal of modern physics a

QCD Factorization Based on Six-Quark Operator Effective Hamiltonian from  Perturbative QCD and Charmless Bottom Meson Decays $B_{(s)}\to \pi\pi,\pi K,  KK$