Contribution of b → sgg through the QCD anomaly in exclusive decays B^± → (η′,η)(K^±,K^{* ±}) and B⁰ → (η′,η)(K⁰,K^{* 0})

We compute the decay rates for the exclusive decays B^± → (η′,η)(K^±,K^{* ±}) and B⁰ → (η′,η)(K⁰,K^{* 0}) in a QCD-improved factorization framework by including the contribution from the process b → sgg → s(η′,η) through the QCD anomaly. This method provides an alternative estimate of the contribution b → scc̄ → s(η′,η) to these decays as compared to the one using the intrinsic charm content of the η′ and η mesons determined through the decays J/ψ → (η,η′,η_c)γ. The advantage of computing the relevant matrix elements via the QCD anomaly governing the transition gg → (η′,η) is that there is no sign ambiguity in these contributions relative to the matrix elements from the rest of the operators in the weak effective Hamiltonian. Numerically, the QCD anomaly method and the one using the radiative decays J/ψ → (η,η′,η_c)γ give similar branching ratios for the decays of interest here. The resulting branching ratios are compared with the CLEO data on B^± → η′K^± and B⁰ → η′K⁰ and predictions are made for the rest.