Two-Body Charmless B Decays Involving eta and eta'

We discuss implications of recent experimental data for B decays into two pseudoscalar mesons, with emphasis on those with $\eta$ and $\eta'$ in the final states. Applying a U-spin argument, we show that tree and penguin amplitudes, both in $B^+ \to \pi^+ \eta$ and in $B^+ \to \pi^+ \eta'$, are of comparable magnitudes. Nontrivial relative weak and strong phases between the tree-level amplitudes and penguin-loop amplitudes in the $B^{\pm} \to \pi^{\pm} \eta$ modes are extracted. We predict possible values for the averaged branching ratio and CP asymmetry of the $B^{\pm} \to \pi^{\pm} \eta'$ modes. We test the assumption of a singlet-penguin amplitude with the same weak and strong phases as the QCD penguin in explaining the large branching ratios of $\eta' K$ modes, and show that it is consistent with current branching ratio and CP asymmetry data of the $B^+ \to (\pi^0, \eta, \eta') K^+$ modes. We also show that the strong phases of the singlet-penguin and tree-level amplitudes can be extracted with further input of electroweak penguin contributions and a sufficiently well-known branching ratio of the $\eta K^+$ mode. Using SU(3) flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.