B→η(′)(l−ν¯l,l+l−,K,K*)decays in the quark-flavor mixing scheme

Abstract

In the quark-flavor mixing scheme, $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ are linear combinations of flavor states ${\ensuremath{\eta}}_{q}=(u\overline{u}+d\overline{d})/\sqrt{2}$ and ${\ensuremath{\eta}}_{s}=s\overline{s}$ 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 $\sqrt{2{m}_{K}^{2}\ensuremath{-}{m}_{\ensuremath{\pi}}^{2}}$ by the approximate flavor symmetry, while ${m}_{qq}$ is found to be $0.18\ifmmode\pm\else\textpm\fi{}0.08\text{ }\text{ }\mathrm{GeV}$. For a large allowed value of ${m}_{qq}$, we show that the branching ratios (BRs) for $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}X$ decays with $X=({\ensuremath{\ell}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}},{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}})$ are enhanced. We also illustrate that $\mathrm{BR}(B\ensuremath{\rightarrow}\ensuremath{\eta}X)>\mathrm{BR}(B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}X)$ in the mechanism without the flavor-singlet contribution. Moreover, we demonstrate that the decay branching ratios for $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}{K}^{[*]}$ are consistent with the data. In particular, the puzzle of the large $\mathrm{BR}(B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}K)$ can be solved. In addition, we find that the $CP$ asymmetry for ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{\ifmmode\pm\else\textpm\fi{}}$ can be as large as $\ensuremath{-}30%$, which agrees well with the data. However, we cannot accommodate the $CP$ asymmetries of $B\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{*}$ in our analysis, which could indicate the existence of some new $CP$ violating sources.