Natural SM-like 126 GeV Higgs boson via nondecoupling 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 minimal supersymmetric standard model, in which SM-like couplings are natural, but raising the Higgs mass to 126 GeV requires a considerable tuning, and the nonminimal supersymmetric standard model, in which the situation is reversed: the Higgs is naturally heavier, but being SM-like requires some tuning. We show that models with nondecoupling 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 reach of LHC run II.