The physics of the $\eta$--${\eta }^{\mathrm{\prime }}$ system versus $B^0\to J\mathrm{/}\mathrm{\Psi }\eta ({\eta }^{\mathrm{\prime }})$ and $B_s\to J\mathrm{/}\mathrm{\Psi }\eta ({\eta }^{\mathrm{\prime }})$ decays

An approach to the properties of the $\eta$–${\eta }^{\mathrm{\prime }}$ system developed to solve the famous $U(1)$ problem is used to calculate the partial widths ratios to $\eta$ and ${\eta }^{\mathrm{\prime }}$ in the $B^0\to J\mathrm{/}\mathrm{\Psi }\eta ({\eta }^{\mathrm{\prime }},{\pi }^0)$ and $B_s\to J\mathrm{/}\mathrm{\Psi }\eta ({\eta }^{\mathrm{\prime }})$ decays. We obtain the results in agreement with the experimental data.