Exploration of elastic scattering rates for supersymmetric dark matter

We explore the possible cross sections for the elastic scattering of neutralinos $\chi$ on nucleons $p,n$ in the minimal supersymmetric extension of the standard model (MSSM). Universality of the soft supersymmetry-breaking scalar masses for the Higgs multiplets is not assumed, but the MSSM parameters are nevertheless required to lead consistently to an electroweak vacuum. We explore systematically the region of MSSM parameter space where CERN LEP and other accelerator constraints are respected, and the relic neutralino density lies in the range $0.1<~{\Omega }_{\chi }{h}^2<~0.3$ preferred by cosmology. We also discuss models with ${\Omega }_{\chi }{h}^2<0.1,$ in which case we scale the density of supersymmetric dark matter in our galactic halo by ${\Omega }_{\chi }{h}^2/0.1,$ allowing for the possible existence of some complementary form of cold dark matter. We restrict our attention to $\tan \beta <~10,$ for which reliable relic-density calculations are available. Within this range of $\tan \beta ,$ we find values of the cross sections that are considerably lower than the present experimental sensitivities. At low neutralino masses, $m_{\chi }\lesssim 100$ GeV, the cross sections may be somewhat higher than in the constrained MSSM with universal soft Higgs boson masses, though they are generally lower. In the case of large $m_{\chi },$ the cross sections we find may be considerably larger than in the constrained model, but still well below the present experimental sensitivity.