Charmless Hadronic Two-body Decays of Bu and Bd Mesons

Two-body charmless nonleptonic decays of Bu and Bd mesons are studied within the framework of generalized factorization in which the effective Wilson coefficients ceff i are renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Contrary to previous studies, our ceff i do not suffer from gauge and infrared problems. Nonfactorizable effects are parametrized in terms of N eff c (LL) and N eff c (LR), the effective numbers of colors arising from (V − A)(V − A) and (V − A)(V + A) four-quark operators, respectively. Tree and penguin transitions are classified into six different classes. The data of B− → ρ0π− and B− → φK− clearly indicate that N eff c (LR) 6= N eff c (LL): The first measurement of the b → u mode B− → ρ0π− and the experimental information on the tree-dominated mode B− → ωπ− all imply that N eff c (LL) is less than 3, whereas the CLEO measurement of B − → φK− shows N eff c (LR) > 3. For given input parameters, the prediction of B(B → η′K) is largely improved by setting N eff c (LL) ∼ 2 and N eff c (LR) > N eff c (LL); in particular, the charm content of the η′ contributes in the right direction. The decay rate of B → φK∗ is very sensitive to the form-factor ratio A2/A1; the absence of B → φK events does not necessarily invalidate the factorization approach. If the branching ratio of B− → ωK− is experimentally found to be significantly larger than that of B− → ρ0K−, we argue that inelastic final-state rescattering may account for the disparity between ωK− and ρ0K−. By contrast, if B(B− → ρ0K−) ∼ B(B− → ωK−) is observed, then W -annihilation and/or spacelike penguins could play a prominent role. The decay modes B 0 d → φπ0, φη, φη′, φρ0, φω, B− → φπ−, φρ− involving a vector meson φ are dominated by electroweak penguins. We show that a unitarity angle γ larger than 90◦ is helpful for explaining the π+π−, πK and η′K data. The relative magnitudes of tree, QCD penguin and electroweak penguin amplitudes are tabulated for all charmless B → PP, V P, V V decays. Our favored predictions for branching ratios are those for N eff c (LL) ≈ 2 and N eff c (LR) ∼ 5.