I discuss a simple gauge extension of the minimal supersymmetric standard model (MSSM), where the fine tuning in the Higgs mass parameters is highly reduced. The Higgs boson is insensitive to high energies because of supersymmetry and also because it is a pseudo-Goldstone boson of a global symmetry (referred to as “double protection” or “super-little Higgs” mechanism). A large shift in the Higgs quartic self coupling is obtained via a non-decoupling D-term coming from an extra gauge group, resulting in a Higgs that can be as heavy as 135 GeV with a tuning milder than 10%. With an appropriate choice of quantum numbers one can achieve that the additional quartic is generated without a corresponding shift in the Higgs mass, thus preserving the double protection of the Higgs. I will also comment on the possibility of a stealth Higgs.

CERN-TH