Revisiting Charmless Two-Body B Decays involving ${\eta }^{\prime }$ and $\eta$

Abstract

We have studied charmless two-body B decays involving $\eta$ and ${\eta }^{\prime }$ in the framework of QCD improved factorization appraoch. The spectator hard scattering mechanism for ${\eta }^{\prime }$ production have been re-examined and extended, which contributions are incorporated consistently into the factorizable leading contributions. It is found that the conventional mechanism would give $Br(B\to {\eta }^{\prime }K)\sim 30\times 10^{-6}$ which agrees with predictions based on naive factorization approaches. With the incorporation of spectator hard scattering mechanism contributions, theoretical predictions are improved much and the bulk of $Br(B\to {\eta }^{\prime }K)$ are accommodated in the reasonable parameter space. We have also presented calculations of $g^{\ast }{g}^{\ast }-{\eta }^{(\prime )}$ transition form factors within the standard hard scattering approach. It is shown that the new contributions in the modes such as $B\to {\eta }^{\prime }+vector$ and $B\to \eta +\pi ,\rho ,K^{(\ast )}$ are small. Direct CP-violation in those decay modes are predicted. It is shown that the prospects for measuring direct CP-violation effects in $B^{\pm }\to$ ${\eta }^{\prime }{K}^{\pm }$, ${\eta }^{\prime }{\pi }^{\pm }$, $\eta {\pi }^{\pm }$, and $\eta K^{\pm }$ are promising at B factories in the near future.

Comments: 34 pages, 5 figures. Title changed, text polished and some statements softened