Branching Ratio and CP Asymmetry of $B_s\to \rho (\omega )K$ Decays in the Perturbative QCD Approach

Abstract

In this paper, we calculate the branching ratios and CP-violating asymmetries for $B_s\to {\rho }^{\pm }{K}^{\mp }$, $B_s\to {\rho }^0{\bar{K}}^0$ and $B_s\to \omega {\bar{K}}^0$ decays in the perturbative QCD (pQCD) factorization approach. The theoretical predictions for the CP averaged branching ratios of the considered decays are: $Br(B_s\to {\rho }^{\pm }{K}^{\mp })\approx 24.7\times 10^{-6}$, $Br(B_s\to {\rho }^0{\bar{K}}^0)\approx 1.2\times 10^{-7}$ and $Br(B_s\to \omega {\bar{K}}^0)\approx 1.7\times 10^{-7}$; and we also predict very large direct CP-violating asymmetries for the latter two decay modes: $A_{CP}^{dir}({\rho }^{\pm }{K}^{\mp })\approx -12$, $A_{CP}^{dir}({\rho }^0{\bar{K}}^0)\approx -92$, $A_{CP}^{dir}({\omega }^0{\bar{K}}^0)\approx 81$, $A_{CP}^{mix}({\rho }^0{\bar{K}}^0)\approx -36$, and $A_{CP}^{mix}({\omega }^0{\bar{K}}^0)\approx -40$, which can be tested in the forthcoming LHC-b experiments.

21 pages, 6 ps/eps figures, Revtex

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