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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. Sincenone 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 standardmodel. Besides the current-current operators, the contributions from the QCDand electroweak penguin operators are also taken into account. We find that (a)the branching ratio is about $4 \times 10^{-7}$; (b) the penguin diagramsdominate the total contribution; and (c) the direct CP asymmetry is small insize: no more than $3% $; but the mixing-induced CP asymmetry can be as largeas ten percent testable in the near future LHC-b experiments.Comment: 12 pages, 4 figures included, RevTe

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Branching ratio and<i>CP</i>asymmetry of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:…

Branching ratio andCPasymmetry ofBs→π+π−