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We discuss the properties of a model incorporating both a scalar electroweakHiggs doublet and an electroweak Higgs triplet. We construct the low-energyeffective theory for the light Higgs-doublet in the limit of small (butnonzero) deviations in the rho parameter from one, a limit in which the tripletstates become heavy. For small deviations in the rho parameter from one,perturbative unitarity of WW scattering breaks down at a scale inverselyproportional to the renormalized vacuum expectation value of the triplet field(or, equivalently, inversely proportional to the square-root of the deviationof the rho parameter from one). This result imposes an upper limit on themass-scale of the heavy triplet bosons in a perturbative theory; we show thatthis upper bound is consistent with dimensional analysis in the low-energyeffective theory. Recent articles have shown that the triplet bosons do notdecouple, in the sense that deviations in the rho parameter from one do notnecessarily vanish at one-loop in the limit of large triplet mass. We clarifythat, despite the non-decoupling behavior of the Higgs-triplet, this model doesnot violate the decoupling theorem since it incorporates a large dimensionfulcoupling. Nonetheless, we show that if the triplet-Higgs boson masses are oforder the GUT scale, perturbative consistency of the theory requires the(properly renormalized) Higgs-triplet vacuum expectation value to be so smallas to be irrelevant for electroweak phenomenology.

Low-Energy Effective Theory, Unitarity, and Non-Decoupling Behavior in a Model with Heavy Higgs-Triplet Fields