Neutralino dark matter in minimal supergravity: Direct detection versus collider searches

We calculate expected event rates for direct detection of relic neutralinos as a function of parameter space of the minimal supergravity model. Numerical results are presented for the specific case of a ${}^{73}\mathrm{Ge}$ detector. We find significant detection rates $(R>\mathrm{}0.01\mathrm{}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{s}/\mathrm{k}\mathrm{g}/\mathrm{d}\mathrm{a}\mathrm{y})$ in regions of parameter space most favored by constraints from $\overrightarrow{B}{X}_s\gamma$ and the cosmological relic density of neutralinos. The detection rates are especially large in regions of large $\tan \beta ,$ where many conventional signals for supersymmetry at collider experiments are difficult to detect. If the parameter $\tan \beta$ is large, then there is a significant probability that the first direct evidence for supersymmetry could come from direct detection experiments, rather than from collider searches for sparticles.