Neutralino dark matter scattering and B_s to μ^+ μ^- in SUSY models

It is pointed out that there is a strong correlation between the neutralino dark matter scattering cross section $\sigma_{\tilde{\chi} p}$ and the branching ratio for $B_s \to \mu^+ \mu^-$ within minimal supergravity (mSUGRA) and its extensions. This correlation arises mainly from $\tan\beta$ and heavy neutral Higgs mass dependence, and shows a nice interplay between vastly different two observables within supersymmetric models. Current upper limit on $B(B_s \to \mu^+ \mu^-) < 5.8 \times 10^{-7}$ excludes substantial parameter space where $\sigma_{\tilde{\chi} p}$ is within the CDMS sensitivity region.