$B\to {\eta }^{(\prime )}({\ell }^{-}{\bar{\nu }}_{\ell },{\ell }^{+}{\ell }^{-},K,K^{\ast })$ decays in the quark-flavor mixing scheme

Abstract

In the quark-flavor mixing scheme, $\eta$ and ${\eta }^{\prime }$ are linear combinations of 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 is close to $\sqrt{2m_K^2-m_{\pi }^2}$ 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 also illustrate that $BR(B\to \eta X)>BR(B\to {\eta }^{\prime }X)$ in the mechanism without the flavor-singlet contribution. Moreover, we demonstrate that the decay branching ratios (BRs) for $B\to {\eta }^{(\prime )}{K}^{[\ast ]}$ are consistent with 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 $B\to \eta K^{\ast }$ in our analysis, which could indicate the existence of some new CP violating sources.

Comments: 18 pages, 4 figures, typos corrected and version revised, version to appear in Phys. Rev. D