  For the experimental search of neutralino dark matter, it is important to
know its allowed mass and scattering cross section with the nucleon. In order
to figure out how light a neutralino dark matter can be predicted in low energy
supersymmetry, we scan over the parameter space of the NMSSM (next-to-minimal
supersymmetric model), assuming all the relevant soft mass parameters to be
below TeV scale. We find that in the parameter space allowed by current
experiments the neutralino dark matter can be as light as a few GeV and its
scattering rate off the nucleon can reach the sensitivity of XENON100 and
CoGeNT. As a result, a sizable parameter space is excluded by the current
XENON100 and CoGeNT data (the plausible CoGeNT dark matter signal can also be
explained). The future 6000 kg-days exposure of XENON100 will further explore
(but cannot completely cover) the remained parameter space. Moreover, we find
that in such a light dark matter scenario a light CP-even or CP-odd Higgs boson
must be present to satisfy the measured dark matter relic density.
Consequently, the SM-like Higgs boson $h_{SM}$ may decay predominantly into a
pair of light Higgs bosons or a pair of neutralinos so that the conventional
decays like $h_{SM} -> \gamma \gamma$ is much suppressed.
