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In the quark-flavor mixing scheme, $\eta$ and $\eta'$ are linear combinationsof flavor states $\eta_{q}=(u\bar{u}+d\bar{d})/\sqrt{2}$ and$\eta_{s}=s\bar{s}$ with the masses of $m_{qq}$ and $m_{ss}$, respectively.Phenomenologically, $m_{ss}$ is strictly fixed to be around 0.69, which isclose to $\sqrt{2m^{2}_{K}-m^{2}_{\pi}}$ by the approximate flavor symmetry,while $m_{qq}$ is found to be $0.18\pm 0.08$ GeV. For a large allowed value of$m_{qq}$, we show that the BRs for $B\to \eta^{(\prime)} X$ decays with$X=(\ell^{-} \bar\nu_{\ell}, \ell^{+} \ell^{-})$ are enhanced. We alsoillustrate that $BR(B\to\eta X)> BR(B\to \eta^{\prime} X)$ in the mechanismwithout the flavor-singlet contribution. Moreover, we demonstrate that thedecay branching ratios (BRs) for $B\to \eta^{(\prime)}K^{[*]}$ are consistentwith the data. In particular, the puzzle of the large $BR(B\to \eta^{\prime}K)$ can be solved. In addition, we find that the CP asymmetry for $B^{\pm}\to\eta K^{\pm}$ can be as large as -30%, which agrees well with the data.However, we cannot accommodate the CP asymmetries of $B\to \eta K^*$ in ouranalysis, which could indicate the existence of some new CP violating sources.Comment: 18 pages, 4 figures, typos corrected and version revised, version to  appear in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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