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We consider $B_s \to \mu^+ \mu^-$ and the muon $(g-2)_\mu$ in various SUSYbreaking mediation mechanisms. If the decay $B_s \to \mu^+ \mu^-$ is observedat Tevatron Run II with a branching ratio larger than $\sim 2 \times 10^{-8} $,the noscale supergravity (including the gaugino mediation), the gauge mediationscenario with small number of messenger fields and low messenger scale, and aclass of anomaly mediation scenarios will be excluded, even if they canaccommodate a large muon $(g-2)_\mu$. On the other hand, the minimalsupergravity scenario and similar mechanisms derived from string models canaccommodate this observation.Comment: 4 pages, 3 figure

physical review letters

Implications on Supersymmetry-Breaking Mediation Mechanisms from Observing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and the Muon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math>

Implications on Supersymmetry-Breaking Mediation Mechanisms from ObservingBs→μ+μ−and the Muong−2