Two-body charmlessBdecays involvingηandη′

We discuss the implications of recent experimental data for B decays into two pseudoscalar mesons, with an emphasis on those with $\eta$ and ${\eta }^{\prime }$ in the final states. Applying a U-spin argument, we show that tree and penguin amplitudes, both in $B^{+}\to {\pi }^{+}\eta$ and in $B^{+}\to {\pi }^{+}{\eta }^{\prime },$ 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 the possible values for the averaged branching ratio and CP asymmetry of the $B^{\pm }\to {\pi }^{\pm }{\eta }^{\prime }$ modes. We test the assumption of a singlet-penguin amplitude with the same weak and strong phases as the QCD penguin amplitude in explaining the large branching ratios of ${\eta }^{\prime }K$ modes, and show that it is consistent with current branching ratio and CP asymmetry data of the $B^{+}\to ({\pi }^0,\eta ,{\eta }^{\prime }{)K}^{+}$ 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 $\mathrm{SU}\left(3\right)\mathrm{}$ flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.