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