The semi-constrained NMSSM satisfying bounds from the LHC, LUX and   Planck
  We study the parameter space of the semi-constrained NMSSM, compatible with constraints on the Standard Model like Higgs mass and signal rates, constraints from searches for squarks and gluinos, a dark matter relic density compatible with bounds from WMAP/Planck, and direct detection cross sections compatible with constraints from LUX. The remaining parameter space allows for a fine-tuning as low as about 100, an additional lighter Higgs boson in the 60-120 GeV mass range detectable in the diphoton mode or in decays into a pair of lighter CP-odd Higgs bosons, and dominantly singlino like dark matter with a mass down to 1 GeV, but possibly a very small direct detection cross section. 
Ulrich Ellwanger, Cyril Hugonie
hep-ph