Tree-level non-decoupling and the supersymmetric Higgs sector

Because of the existence of cubic scalar couplings, there are, in general nondecoupling effects at tree level in the scalar sector of any theory with two or more very different mass scales. We show this explicitly in the minimal non-supersymmetric SU(5) model of grand unification. We then point out that the matching condition of quartic scalar couplings in their evolution as functions of energy Scale is fundamentally different from that of gauge or Yukawa couplings. We show also how tree-level decoupling is guaranteed if supersymmetry is imposed. On the other hand, if the gauge symmetry is larger than that of the standard model at the mass scale of supersymmetry breaking, the two-Higgs-doublet structure at the presumably lower electroweak energy scale will be different from that of the minimal supersymmetric standard model, as has already been shown previously in a number of specific examples. We add here one example involving four Higgs doublers.