We study the constraints on neutralino dark matter in minimal low energy supersymmetry models and the case of heavy lepton and quark scalar superpartners. For values of the Higgsino and gaugino mass parameters of the order of the weak scale, direct detection experiments are already putting strong bounds on models in which the dominant interactions between the dark matter candidates and nuclei are governed by Higgs boson exchange processes, particularly for positive values of the Higgsino mass parameter mu. For negative values of mu, there can be destructive interference between the amplitudes associated with the exchange of the standard CP-even Higgs boson and the exchange of the non-standard one. This leads to specific regions of parameter space which are consistent with the current experimental constraints and a thermal origin of the observed relic density. In this article we study the current experimental constraints on these scenarios, as well as the future experimental probes, using a combination of direct and indirect dark matter detection and heavy Higgs and electroweakino searches at hadron colliders.

32 pages, 13 figures