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

• Received 13 November 2007

DOI:https://doi.org/10.1103/PhysRevD.78.074030