QCD Anomaly Coupling for the ${\eta }^{\prime }-g-g$ Vertex in Inclusive Decay $B\to {\eta }^{\prime }{X}_s$

Abstract

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

9 pages, latex, one figure included