Charmless Hadronic Two-body Decays of B_u and B_d Mesons
Two-body charmless nonleptonic decays of B_u and B_d mesons are studied within the framework of generalized factorization in which the effective Wilson coefficients $c^{eff}_i$ are renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Contrary to previous studies, our $c_i^{eff}$ do not suffer from gauge and infrared problems. Nonfactorizable effects are parametrized in terms of N_c(LL) and N_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 $B^-\toρ^0π^-$ and $B^-\toϕK^-$ clearly indicate that $N_c(LR)\neq N_c(LL)$: The first measurement of the b -> u mode $B^-\toρ^0π^-$ and the experimental information on the tree-dominated mode $B^-\toωπ^-$ all imply that Nc(LL) is less than 3, whereas the CLEO measurement of $B^-\toϕK^-$ shows Nc(LR)>3. For given input parameters, the prediction of ${\cal B}(B\toη' K)$ is largely improved by setting Nc(LL)~2 and Nc(LR)>Nc(LL); in particular, the charm content of the eta' contributes in the right direction. The decay rate of $B\toϕK^*$ is very sensitive to the form-factor ratio A_2/A_1; the absence of $B\toϕK$ events does not necessarily invalidate the factorization approach. If the branching ratio of $B^-\toωK^-$ is experimentally found to be significantly larger than that of $B^-\toρ^0 K^-$, we argue that inelastic final-state rescattering may account for the disparity between $ωK^-$ and $ρ^0 K^-$.