B-decays at Large $\tan \beta$ as a Probe of SUSY Breaking

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 $\sim 2\times {10}^{-8}$, the noscale supergravity (including the gaugino mediation), the gauge mediation scenario with 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.