Correlation of $B_{s} \to \mu^{+}\mu^{-}$ and $(g-2)_{mu}$ in minimal supergravity

We analyse the rare decay mode B_s -> mu^+ mu^- in the minimal supergravity scenario (mSUGRA). We find a strong correlation with the muon anomalous magnetic moment (g-2)_mu. An interpretation of the recently measured excess in (g-2)_mu in terms of mSUGRA corrections implies a substantial supersymmetric enhancement of the branching ratio Br(B_s -> mu^+ mu^-): if (g-2)_mu exceeds the Standard Model prediction by 3*10^{-9}, Br(B_s -> mu^+ mu^-) is larger by a factor of 100 than in the Standard Model and well within reach of Run-II of the Tevatron. Thus an experimental search for B_s -> mu^+ mu^- is a stringent test of the mSUGRA GUT scale boundary conditions. If the decay B_s -> mu^+ mu^- is observed at Run-II of the Tevatron, then we predict the mass of lightest supersymmetric Higgs boson to be less than 118 GeV. The decay B_s -> mu^+ mu^- can also significantly probe the favoured parameter range in SO(10) SUSY GUT models, possibly excluding them.