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

We consider $B_s\to {\mu }^{+}{\mu }^{-}$ and the muon $(g-2{)}_{\mu }$ in various supersymmetry-breaking mediation mechanisms. If the decay $B_s\to {\mu }^{+}{\mu }^{-}$ is observed at Tevatron Run II with a branching ratio larger than $\sim 2\times {10}^{-8}$, the noscale supergravity (including the gaugino mediation), the gauge mediation scenario with a small number of messenger fields and low messenger scale, and a class of anomaly mediation scenarios will be 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.