Further Analysis of Di-gluon Fusion Mechanism for the decays of $B\to K{\eta }^{\mathrm{\prime }}$

Di-gluon fusion mechanism might account for the large branching ratios of $B\to K{\eta }^{\mathrm{\prime }}$. But because we know little about the effective ${\eta }^{\mathrm{\prime }}gg$ vertex, there are large uncertainties in perturbative QCD estimations. In this paper, we try several kinds of ${\eta }^{\mathrm{\prime }}gg$ form factors and compare the numerical results with the experiment. We find that, though we know little about ${\eta }^{\mathrm{\prime }}gg$ form factor, if di-gluon fusion mechanism is important in $B\to K{\eta }^{\mathrm{\prime }}$, the branching ratios of the decays $B\to K^{\ast }{\eta }^{\mathrm{\prime }}$ would be around ${10}^{-5}$ which can be tested by future experiments.