We perform a comparative study of the neutralino dark matter scattering on nucleon in three popular supersymmetric models: the minimal (MSSM), the next-tominimal (NMSSM) and the nearly minimal (nMSSM). First, we give the predictions of the elastic cross section by scanning over the parameter space allowed by various direct and indirect constraints, which are from the measurement of the cosmic dark matter relic density, the collider search for Higgs boson and sparticles, the precision electroweak measurements and the muon anomalous magnetic moment. Then we demonstrate the property of the allowed parameter space with/without the new limits from CDMS II. We obtain the following observations: (i) For each model the new CDMS limits can exclude a large part of the parameter space allowed by current collider constraints; (ii) The property of the allowed parameter space is similar for MSSM and NMSSM, but quite different for nMSSM; (iii) For each model the future SuperCDMS can cover most of the allowed parameter space given that all soft breaking parameters are below 1TeV.
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