Contribution of $b\to s gg$ through the QCD anomaly in exclusive decays $B \to (\eta',\eta) (K, K^{*})$

Abstract

The charm content in $\eta'$ is estimated using the QCD U(1) axial anomaly applied to $b\to s g g \to \eta' s$. We find $f_{\eta'}^{(c)} \approx - 3.1$ MeV for $m_c = 1.3$ GeV. Our estimate agrees with other independent methods by Feldmann and Kroll, and Araki, Musakhanov and Toki. The resulting branching ratios for $B \to \eta' K$ in the generalized factorization model are marginally consistent with the CLEO data, although they are lower than the data by $\sim 2$.