  Since the recent results of direct detection experiments at low mass, many
authors have revisited the case of light (1 -10) GeV WIMPs. In particular,
there have been a few attempts to explain the results from the DAMA/LIBRA, CDMS
and/or CoGeNT experiments by invoking neutralinos lighter than 15 GeV. Here we
show that in the MSSM, such light particles are completely ruled out by the
TEVATRON limits on the mass of the pseudoscalar Higgs. On the contrary, in the
NMSSM, we find that light neutralinos could still be viable candidates. In
fact, in some cases, they may even have an elastic scattering cross section on
nucleons in the range that is needed to explain either the DAMA/LIBRA, CoGeNT
or CDMS recent results. Finally, we revisit the lowest limit on the neutralino
mass in the MSSM and find that neutralinos should be heavier than ~28 GeV to
evade present experimental bounds.
