Branching ratio and CP asymmetry of $B_s\to {\pi }^{+}{\pi }^{-}$ decays in the perturbative QCD approach

Abstract

In this paper, we calculate the decay rate and CP asymmetry of the $B_s\to {\pi }^{+}{\pi }^{-}$ decay in perturbative QCD approach with Sudakov resummation. Since none of the quarks in final states is the same as those of the initial $B_s$ meson, this decay can occur only via annihilation diagrams in the standard model. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. We find that (a) the branching ratio is about $4\times 10^{-7}$; (b) the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is small in size: no more than $3$; but the mixing-induced CP asymmetry can be as large as ten percent testable in the near future LHC-b experiments.

Comments: 12 pages, 4 figures included, RevTeX