Okubo-Zweig-Iizuka-rule violation and B\to \eta^{(\prime)}K branching ratios

Abstract

We show that few-percent Okubo-Zweig-Iizuka-rule violating effects in the quark-flavor basis for the $\eta$-$\eta'$ mixing can enhance the chiral scale associated with the $\eta_q$ meson few times. This enhancement is sufficient for accommodating the dramatically different data of the $B\to\eta^{\prime} K$ and $B\to\eta K$ branching ratios. We comment on other proposals for resolving this problem, including flavor-singlet contributions, axial U(1) anomaly, and nonperturbative charming penguins. Discrimination of the above proposals by means of the $B\to\eta^{(\prime)}\ell\nu$ and $B_s\to\eta^{(\prime)}\ell\ell$ data is suggested.