Neutralino Proton Cross Sections In Supergravity Models

The neutralino-proton cross section is examined for supergravity models with R-parity invariance with universal and non-universal soft breaking. The region of parameter space that dark matter detectors are currently (or will be shortly) sensitive i.e. $(0.1-10)\times {10}^{-6}$ pb, is examined. For universal soft breaking (mSUGRA), detectors with sensitivity ${\sigma }_{{\tilde{\chi }}_1^0-p}\ge 1\times {10}^{-6}$ pb will be able to sample parts of the parameter space for $\tan \beta 25$. Current relic density bounds restrict $m_{{\tilde{\chi }}_1^0}\le 120$ GeV for the maximum cross sections, which is below where astronomical uncertainties about the Milky Way are relevant. Nonuniversal soft breaking models can allow much larger cross sections and can sample the parameter space for $\tan \beta \stackrel{>}{\sim} 4$\mathrm{.}Insuchmodels,$m_0$ can be quite large reducing the tension between proton decay bounds and dark matter analysis. We note the existance of two new domains where coannihilation effects can enter, i.e. for mSUGRA at large $\tan \beta$, and for nonuniversal models with small $\tan \beta$.