The Higgs Sector and CoGeNT/DAMA-Like Dark Matter in Supersymmetric
  Models
  Recent data from CoGeNT and DAMA are roughly consistent with a very light
dark matter particle with $m\sim 4-10\gev$ and spin-independent cross section
of order $\sigma_{SI} \sim (1-3)\times 10^{-4}\pb$. An important question is
whether these observations are compatible with supersymmetric models obeying
$\Omega h^2\sim 0.11$ without violating existing collider constraints and
precision measurements. In this talk, I review the fact the the Minimal
Supersymmetric Model allows insufficient flexibility to achieve such
compatibility, basically because of the highly constrained nature of the MSSM
Higgs sector in relation to LEP limits on Higgs bosons. I then outline the
manner in which the more flexible Higgs sectors of the Next-to-Minimal
Supersymmetric Model and an Extended Next-to-Minimal Supersymmetric Model allow
large $\sigma_{SI}$ and $\Omega h^2\sim 0.11$ at low LSP mass without violating
LEP, Tevatron, BaBar and other experimental limits. The relationship of the
required Higgs sectors to the NMSSM "ideal-Higgs" scenarios is discussed.
