Charmless Hadronic Two-body Decays of the B_s Mesons

Abstract

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 $\mu$ 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 $B_s\to \eta \pi ,{\eta }^{\prime }\pi ,\eta \rho ,{\eta }^{\prime }\rho ,\varphi \pi ,\varphi \rho$, 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 $B_s\to \eta {\eta }^{\prime }$ is of order 2x10^{-5}, (iv) the contribution from the ${\eta }^{\prime }$ charm content is important for $B_s\to {\eta }^{\prime }{\eta }^{\prime }$, but less significant for $B_s\to \eta {\eta }^{\prime }$, and (v) the decay rates for the final states $K^{+(\ast )}{K}^{-(\ast )}$ follow the pattern: $\Gamma (B_s\to K^{+}{K}^{-})>\Gamma (B_s\to K^{+}{K}^{\ast -})\ge \Gamma (B_s\to K^{\ast +}{K}^{\ast -})>\Gamma (B_s\to K^{+\ast }{K}^{-})$, as a consequence of various interference effects between the penguin amplitudes governed by the coefficients a_4 and a_6.

29 pages. Table V is revised and a typo in Eq.(3.3) is corrected. To appear in Phys. Rev. D

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