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The parameter space of the simplest extension of the standard model, isstudied in the light of the 125 GeV Higgs boson discovery. The Hill modelextends the scalar sector of the standard model with a real singlet, that mixeswith the SM Higgs boson. The two-loop SM renormalization group equations arecompleted with the one-loop Hill equations. Stability up to the Planck scale ispossible without tension with the other parameters. An extension with moresinglet fields, in particular a higher dimensional (HEIDI) field is presented.

A renormalization group analysis of the Hill model and its HEIDI extension