  We study the neutralino being the Lightest Supersymmetric Particle (LSP) as a
cold Dark Matter (DM) candidate with a mass less than 40 GeV in the framework
of the Next-to-Minimal-Supersymmetric-Standard-Model (NMSSM). We find that with
the current collider constraints from LEP, the Tevatron and the LHC, there are
three types of light DM solutions consistent with the direct/indirect searches
as well as the relic abundance considerations: (i) A1, H1-funnels, (ii) stau
coannihilation and (iii) sbottom coannihilation. Type-(i) may take place in any
theory with a light scalar (or pseudo-scalar) near the LSP pair threshold;
while Type-(ii) and (iii) could occur in the framework of
Minimal-Supersymmetric-Standard-Model (MSSM) as well. We present a
comprehensive study on the properties of these solutions and point out their
immediate relevance to the experiments of the underground direct detection such
as superCDMS and LUX/LZ, and the astro-physical indirect search such as
Fermi-LAT. We also find that the decays of the SM-like Higgs boson may be
modified appreciably and the new decay channels to the light SUSY particles may
be sizable. The new light CP-even and CP-odd Higgs bosons will decay to a pair
of LSPs as well as other observable final states, leading to interesting new
Higgs phenomenology at colliders. For the light sfermion searches, the signals
would be very challenging to observe at the LHC given the current bounds.
However, a high energy and high luminosity lepton collider, such as the ILC,
would be able to fully cover these scenarios by searching for events with large
missing energy plus charged tracks or displaced vertices.
