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

We study $B\to J\mathrm{/}\mathrm{\Psi }{\eta }^{(\mathrm{\prime })}$ decays and suggest two methods to determine the $\eta -{\eta }^{\mathrm{\prime }}$ 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 $B\to J\mathrm{/}\mathrm{\Psi }\eta$ which is consistent with recent experimental data and predict the branching ratio of $B\to J/\Psi \eta^{\prime}$tobe$7.59\times 10^{-6}$\mathrm{.}Twomethodsfordetermining$\eta-\eta^{\prime}$ mixing angle are suggested in this paper. For the first method, we get the $\eta -{\eta }^{\mathrm{\prime }}$ 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 $\eta -{\eta }^{\mathrm{\prime }}$ mixing angle with better accuracy but needs, as an input, the branching ratio for $B\to J\mathrm{/}\mathrm{\Psi }{\eta }^{\mathrm{\prime }}$which should be measured in the near future.