Study of $B_{s}\to \pi \rho$ decays in the perturbative QCD approach

In this note, we calculate the branching ratio and CP asymmetry parameters of $B_s\to\pi\rho$ in the framework of perturbative QCD approach based on $k_T$ factorization. This decay can occur only via annihilation diagrams in the Standard Model. We find that (a)the charge averaged $Br(B_s\to\pi^{+}\rho^{-}+\pi^{-}\rho^{+})$ is about $(9-12)\times10^{-7}$; $Br(B_s\to\pi^{0}\rho^{0}) \simeq 4\times10^{-7}$; and (b) there are sizable CP asymmetries in the processes, which can be tested in the near future Large Hadron Collider beauty experiments (LHC-b) at CERN or BTeV experiments at Fermilab.