Charmless B Decays to η ′ and η Hai

Exclusive charmless B decays to η and η are studied in the standard effective Hamiltonian approach. The effective coefficients that take into account nonfactorizable effects in external and internal W -emission amplitudes are fixed by experiment. Factorization is applied to the matrix elements of QCD, electroweak penguin operators and next-to-leading corrections to penguin Wilson coefficients, which are renormalization-scheme dependent, are included, but the resultant amplitude is renormalization-scheme and -scale independent. We show that the unexpectedly large branching ratio of B → ηK measured by CLEO can be explained by the Cabibbo-allowed internal W emission process b → cc̄s followed by a conversion of the cc̄ pair into the η via gluon exchanges characterized by a decay constant of order −50 MeV. Implications are discussed. The mechanism of the transition cc̄ → η, if correct, will enhance the decay rates of B → ηK by more than an order of magnitude. However, it plays only a minor role to the rare decays B → η(η)π(ρ). The predicted branching ratio of B → ηπ for positive ρ is marginally ruled out by experiment, indicating that the favored Wolfenstein parameter ρ is negative.