A natural SM-like 126 GeV Higgs via non-decoupling D-terms
  Accommodating both a 126 GeV mass and Standard Model (SM) like couplings for the Higgs has a fine tuning price in supersymmetric models. Examples are the MSSM, in which SM-like couplings are natural, but raising the Higgs mass up to 126 GeV requires a considerable tuning, or the NMSSM, in which the situation is reversed: the Higgs is naturally heavier, but being SM-like requires some tuning. We show that models with non-decoupling D-terms alleviate this tension - a 126 GeV SM-like Higgs comes out basically with no fine tuning cost. In addition, the analysis of the fine tuning of the extended gauge sector shows that naturalness requires the heavy gauge bosons to likely be within the LHC run II reach. 
Enrico Bertuzzo and Claudia Frugiuele
hep-ph