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

Abstract

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 QCD facorization scheme but also the nonfactorizable hard spectator corrections in 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 $\eta -{\eta }^{\prime }$ mixing angle are suggested in this paper. For the first method, we get the $\eta -{\eta }^{\prime }$ mixing angle to be about $-13.1^{\circ }$, which is in consistency with others in the literature. The second method depends on less parameters so can be used to determine the $\eta -{\eta }^{\prime }$ 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.

Comments: 16pages,4figures