The Lower bound on the neutralino nucleon cross-section

We examine if there is a lower bound on the direct detection cross section for the neutralino dark matter in the MSSM. If we impose the minimal supergravity boundary conditions as well as the "naturalness" condition, in particular m_{1/2} < 300 GeV, we show that there is a lower bound of 10^{-46}cm^2 on the cross section for neutralino scattering off of a proton. We also clarify the origin for the lower bound. Relaxing either of the assumptions, however, can lead to much smaller cross sections.