Can neutralinos in the MSSM and NMSSM scenarios still be light?

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.