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 $\eta$ 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 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 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 SU(3) flavor symmetry, we also estimate required data samples to detect modes that have not yet been seen.

Comments: 16 pages, 7 figures, to be submitted to Phys. Rev. D (v1); some remarks and references added (v2); more references added (v3)