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The study of $B\to J/Ψη^{(\prime)}$ decays and determination of $η-η^{\prime}$ mixing angle

We study $B\to J/Ψη^{(\prime)}$ decays and suggest two methods to determine the $η-η^{\prime}$ mixing angle. We calculate not only the factorizable contribution in QCD facorization scheme but also the nonfactorizable hard spectator corrections in pQCD approach. We get the branching ratio of $B\to J/Ψη$ which is consistent with recent experimental data and predict the branching ratio of $B\to J/Ψη^{\prime}$ to be $7.59\times 10^{-6}$. Two methods for determining $η-η^{\prime}$ mixing angle are suggested in this paper. For the first method, we get the $η-η^{\prime}$ mixing angle to be about $-13.1^{\circ}$, which is in consistency with others in the literature. The second method depends on less parameters so can be used to determine the $η-η^{\prime}$ mixing angle with better accuracy but needs, as an input, the branching ratio for $B\to J/Ψη^{\prime}$which should be measured in the near future.