Implications on SUSY breaking mediation mechanisms from observing $B_s \to μ^+ μ^-$ and the muon $(g-2)$

We consider $B_s \to \mu^+ \mu^-$ and the muon $(g-2)_\mu$ in various SUSY breaking mediation mechanisms. If the decay $B_s \to \mu^+ \mu^-$ is observed at Tevatron Run II with a branching ratio larger than $2 \times 10^{-8} $, the noscale supergravity (including the gaugino mediation), the gauge mediation scenario with small number of messenger fields and the minimal anomaly mediation scenarios are excluded, even if they can accommodate a large muon $(g-2)_\mu$. On the other hand, the minimal supergravity scenario and similar mechanisms derived from string models can accommodate this observation.