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

Abstract

We have studied charmless two-body B decays involving $η$ and $η'$ in the framework of QCD improved factorization appraoch. The spectator hard scattering mechanism for $η'$ 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 $Br(B\to η' K)\sim 30\times 10^{-6}$ 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 $Br(B\to η' K)$ are accommodated in the reasonable parameter space. We have also presented calculations of $g^{\ast}g^{\ast}-η^{(\prime)}$ transition form factors within the standard hard scattering approach. It is shown that the new contributions in the modes such as $B\to η' +vector$ and $B\to η+ π, ρ, K^{(\ast)}$ are small. Direct CP-violation in those decay modes are predicted. It is shown that the prospects for measuring direct CP-violation effects in $B^{\pm} \to$ $η' K^{\pm}$, $η' π^{\pm}$, $ηπ^{\pm}$, and $ηK^{\pm}$ are promising at B factories in the near future.