Correlation of $B_s\mathit{}\to \mathit{}{\mu }^{+}{\mu }^{-}$ and $(\mathit{g}-2\mathrm{}{)}_{\mathit{\mu }}$ in Minimal Supergravity

We analyze the decay mode $B_s\to {\mu }^{+}{\mu }^{-}$ in minimal supergravity (mSUGRA). We find that the recently measured excess in $(g-2\mathrm{}{)}_{\mu }$, if interpreted within mSUGRA, is correlated with a substantial enhancement of the branching ratio $B(B_s\to {\mu }^{+}{\mu }^{-})$: if $(g-2\mathrm{}{)}_{\mu }$ exceeds the standard model prediction by $4\times {10}^{-9\mathrm{}}$, $B(B_s\to {\mu }^{+}{\mu }^{-})$ is larger by a factor of 10–100 and within reach of Run-II of the Tevatron. Thus the search for $B_s\to {\mu }^{+}{\mu }^{-}$ is a stringent test of the GUT scale relations of mSUGRA. An observation of $B_s\to {\mu }^{+}{\mu }^{-}$ at the Tevatron implies a mass of the lightest SUSY Higgs boson below 120 GeV. $B_s\to {\mu }^{+}{\mu }^{-}$ can also significantly probe SO(10) SUSY GUT models.