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An approach to the properties of the $\eta$--$\eta'$ system developed tosolve the famous $U(1)$ problem is used to calculate the partial widths ratiosto $\eta$ and $\eta'$ in the $B^0 \rightarrow J/\Psi \ \eta(\eta',\ \pi^0)$ and$B_s \rightarrow J/\Psi \ \eta(\eta')$ decays. We obtain the results inagreement with the experimental data.

The physics of the $\eta$--$\eta'$ system versus $B^0 \rightarrow J/\Psi \ \eta (\eta')$ and $B_s \rightarrow J/\Psi \ \eta (\eta')$ decays