Contribution of $b \to sgg$ through the QCD anomaly in exclusive decays $B^\pm \to (η',η)(K^\pm,K^{*\pm})$ and $B^0 \to (η',η)(K^0,K^{*0})$

Abstract

We compute the decay rates for the exclusive decays $B^{\pm} \to (\eta^{\prime},\eta) (K^{\pm}, K^{*\pm})$ and $B^{0}\to (\eta^{\prime},\eta) (K^{0}, K^{*0})$ in a QCD-improved factorization framework by including the contribution from the process $b\to sgg \to s (\eta^{\prime}, \eta)$ through the QCD anomaly. This method provides an alternative estimate of the contribution $b \to s c\bar{c} \to s(\eta,\eta^\prime)$ to these decays as compared to the one using the intrinsic charm content of the $\eta^{\prime}$ and $\eta$ mesons. The advantage of computing the relevant matrix elements via the QCD anomaly is that there is no sign ambiguity in these contributions. Numerically, the QCD anomaly method and the one using the radiative decays $J/\psi \to (\eta,\eta^{\prime},\eta_c) \gamma$ give similar branching ratios for the decays of interest here. The resulting branching ratios are compared with the CLEO data.