  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.
