Abstract :
Using the next-to-leading order QCD-corrected effective Hamiltonian, charmless exclusive nonleptonic decays of the Bs meson into η or η′ are calculated within the generalized factorization approach. Nonfactorizable contributions, which can be parameterized in terms of the effective number of colors Nceff for PP and VP decay modes, are studied in two different schemes: (i) the one with the “homogeneous” structure in which (Nceff)1≈(Nceff)2≈⋯≈(Nceff)10 are assumed, and (ii) the “heterogeneous” one in which the possibility of Nceff(V+A)≠Nceff(V−A) is considered, where Nceff(V+A) denotes the effective value of colors for the (V−A)(V+A) penguin operators while Nceff(V−A) for the (V−A)(V−A) ones. For processes depending on the Nceff-stable ai such as Bs→(π,ρ)(η′,η), the predicted branching ratios are not sensitive to the factorization approach we choose. While for the processes depending on the Nceff-sensitive ai such as Bs→ωη(′), there is a wide range for the branching ratios depending on the choice of the Nceff involved. We have included the QCD anomaly effect in our calculations and found that it is important for Bs→η(′)η(′). The effect of the (cc̄)→η′ mechanism is found to be tiny due to a possible CKM-suppression and the suppression in the decay constants except for the Bs→φη decay within the “naive” factorization approach, where the internal W diagram is CKM-suppressed and the penguin contributions compensate.
