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Charmless Hadronic Two-body Decays of the B_s Mesons

Two-body charmless nonleptonic decays of the B_s 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_c(LL) and N_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 $B_s\to PP,PV,VV$ decays are calculated as a function of N_c(LR) with two different considerations for N_c(LL). We find that (i) the electroweak penguin contributions account for about 85% (for N_c(LL)=2) of the decay rates of $B_s\to ηπ,η'π,ηρ,η'ρ,ϕπ,ϕρ$, which receive contributions only from tree and electroweak penguin diagrams; a measurement of them will provide a clean determination of the electroweak penguin coefficient a_9, (ii) electroweak penguin corrections to $B_s\toω\etapp,ϕη,ωϕ,K^{(*)}ϕ,ϕϕ$ are in general as significant as QCD penguin effects and even play a dominant role; their decay rates depend strongly on N_c(LR), (iii) the branching ratio of $B_s\to ηη'$ is of order 2x10^{-5}, (iv) the contribution from the $η'$ charm content is important for $B_s\toη'η'$, but less significant for $B_s\toηη'$, and (v) the decay rates for the final states $K^{+(*)}K^{-(*)}$ follow the pattern: $Γ(B_s\to K^+K^-)>Γ(B_s\to K^+K^{*-})\geqΓ(B_s\to K^{*+}K^{*-}) >Γ(B_s\to K^{+*}K^-)$, as a consequence of various interference effects between the penguin amplitudes governed by the coefficients a_4 and a_6.