Decay Constant Ratios $f_{{\eta }_c}\mathrm{/}{f}_{J\mathrm{/}\psi }$ and $f_{{\eta }_b}\mathrm{/}{f}_{\mathrm{{\rm Y}}}$

We calculate the decay constant ratios $f_{{\eta }_c}\mathrm{/}{f}_{J\mathrm{/}\psi }$ and $f_{{\eta }_b}\mathrm{/}{f}_{\mathrm{{\rm Y}}}$. In the calculation we take into account the mock meson structures of the mesons, as well as the difference of the wave functions at origin of the vector and pseudoscalar mesons studied by Ahmady and Mendel. We find that the different spin structures of the mesons much affect the ratios. We incorporate our results in the prediction of the branching ratios of $B\to K \eta_c$.