Charmless Hadronic Two-body Decays of Bs Mesons

Two-body charmless nonleptonic decays of the Bs meson are studied within the framework of generalized factorization in which factorization is applied to the tree level matrix elements while the effective Wilson coefficients are μ and renormalization scheme independent, and nonfactorizable effects are parametrized in terms of N eff c (LL) and N eff c (LR), the effective numbers of colors arising from (V − A)(V − A) and (V − A)(V + A) four-quark operators, respectively. Branching ratios of Bs → PP,PV, V V decays (P : pseudoscalar meson, V : vector meson) are calculated as a function of N eff c (LR) with two different considerations for N eff c (LL): (a) N eff c (LL) being fixed at the value of 2, and (b) N eff c (LL) = N eff c (LR). Tree and penguin transitions are classified into six different classes. We find that (i) the electroweak penguin contributions account for about 85% (for N eff c (LL) = 2) of the decay rates of Bs → ηπ, η′π, ηρ, η′ρ, φπ, φρ, which receive contributions only from tree and electroweak penguin diagrams; a measurement of them will provide a clean determination of the electroweak penguin coefficient a9, (ii) electroweak penguin corrections to Bs → ωη(), φη, ωφ,K(∗)φ, φφ are in general as significant as QCD penguin effects and even play a dominant role; their decay rates depend strongly on N eff c (LR), (iii) the branching ratio of Bs → ηη′, the analogue of Bd → η′K, is of order 2× 10−5, which is only slightly larger than that of η′η′,K∗+ρ−,K+K−,K0K decay modes, (iv) the contribution from the η′ charm content is important for Bs → η′η′, but less significant for Bs → ηη′, and (v) the decay rates for the final states K+(∗)K−(∗) follow the pattern: Γ(Bs → K+K−) > Γ(Bs → K+K∗−) >∼ Γ(Bs → K∗+K∗−) > Γ(Bs → K+∗K−) and likewise for K0(∗)K0(∗), as a consequence of various interference effects between the penguin amplitudes governed by the effective QCD penguin coefficients a4 and a6.