Two-Body Charmless B Decays Involving eta and eta'

Abstract

We discuss implications of recent experimental data for B decays into two pseudoscalar mesons, with emphasis on those with $η$ and $η'$ in the final states. Applying a U-spin argument, we show that tree and penguin amplitudes, both in $B^+ \to π^+ η$ and in $B^+ \to π^+ η'$, are of comparable magnitudes. Nontrivial relative weak and strong phases between the tree-level amplitudes and penguin-loop amplitudes in the $B^{\pm} \to π^{\pm} η$ modes are extracted. We predict possible values for the averaged branching ratio and CP asymmetry of the $B^{\pm} \to π^{\pm} η'$ 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 $η' K$ modes, and show that it is consistent with current branching ratio and CP asymmetry data of the $B^+ \to (π^0, η, η') K^+$ 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 $ηK^+$ mode. Using SU(3) flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.