Branching ratio and CP violation of $B_{s}\to \pi K$ decays in the perturbative QCD approach

Abstract

In the framework of perturbative QCD approach, we calculate the branching ratio and CP asymmetry for $B_{s}^0(\bar{B}_{s}) \to \pi^{\pm} K^\mp$ and $B_{s}(\bar{B}_{s})\to \pi^{0}\bar{K}^{0}(K^{0})$ decays. Besides the usual factorizable diagrams, both non-factorizable and annihilation type contributions are taken into account. We find that (a) the branching ratio of $B_{s}^0(\bar{B}_{s}) \to \pi^{\pm} K^\mp$ is about $(6-10) \times 10^{-6}$; $Br(B_{s}(\bar{B}_{s})\to \pi^{0}\bar{K}^{0}(K^{0}))$ about $ (1-3) \times 10^{-7}$; and (b) there are large CP asymmetries in the two processes, which can be tested in the near future LHC-b experiments at CERN and BTeV experiments at Fermilab.