Neutralino Dark Matter in minimal supersymmetric standard model with natural light Higgs sector

We study the neutralino relic density in the minimal supersymmetric standard model with natural light Higgs sector in which all Higgs masses, the supersymmetry (SUSY) breaking parameters, and the higgsino mass parameter mu are of order the weak scale. To realize this situation we adopt nonuniversal Higgs masses at the grand unified scale. We show that in some parameter space in which the SUSY breaking parameters are comparatively small, not only the constraint from the observed relic density of dark matter but also the LEP Higgs bound and the constraint from the b ->s gamma process are satisfied. In most of the parameter space, the neutralino relic density becomes smaller than the observed relic density in contrast with the results in the constrained minimal SUSY standard model (CMSSM). The reason is that the neutralino coannihilation processes to Higgs bosons open even if the gaugino mass is small and the cross sections become large due to the small dimensionful parameters. Especially small mu parameter and the light CP-odd Higgs, which are difficult to be realized in the CMSSM, are essential for the result.