Charmless B decays to eta' and eta

Abstract

Exclusive charmless B decays to $\eta'$ and $\eta$ are studied in the standard effective Hamiltonian approach. The effective coefficients that take into account nonfactorizable effects in external and internal W-emission amplitudes are fixed by experiment. Factorization is applied to the matrix elements of QCD, electroweak penguin operators and next-to-leading corrections to penguin Wilson coefficients, which are renormalization-scheme dependent, are included, but the resultant amplitude is renormalization-scheme and -scale independent. We show that the unexpectedly large branching ratio of $B^\pm\to \eta' K^\pm$ measured by CLEO can be explained by the Cabibbo-allowed internal W-emission process $b\to c\bar cs$ followed by a conversion of the $c\bar c$ pair into the $\eta'$ via gluon exchanges characterized by a decay constant of order -50 MeV. Implications are discussed. The mechanism of the transition $c\bar c\to\eta'$, if correct, will enhance the decay rates of $B\to \eta' K^{*}$ by more than an order of magnitude. However, it plays only a minor role to the rare decays $B\to \eta'(\eta)\pi(\rho)$. The predicted branching ratio of $B^\pm\to \eta\pi^\pm$ for positive $\rho$ is marginally ruled out by experiment, indicating that the favored Wolfenstein parameter $\rho$ is negative.