Two-body charmlessBdecays involvingηandη′

Abstract

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