QCD Anomaly Coupling for the $\eta'-g-g$ Vertex in Inclusive Decay $B\to\eta' X_s$

Abstract

The QCD anomaly coupling of $\eta'-g-g$ is treated as the axial vector current triangle anomaly. By assuming the divergent axial vector coupling of the $\eta'$ meson with the quark line in the triangle diagram, we calculate the QCD anomaly of $\eta'-g-g$ as well as the QED anomaly of $\eta'-\gamma-\gamma$ with only one common parameter $\kappa_{\eta'}$. We obtain consistent results of the branching ratios for $B\to\eta' X_s, J/\psi\to\eta'\gamma$ and $\eta'\to \gamma\gamma$ when comparing with experimental data.