Electroweak precision data has been extensively used to constrain models
containing physics beyond that of the Standard Model. When the model contains
Higgs scalars in representations other than SU(2) singlets or doublets, and
hence rho not equal to one at tree level, a correct renormalization scheme
requires more inputs than the three needed for the Standard Model. We discuss
the connection between the renormalization of models with Higgs triplets and
the decoupling properties of the models as the mass scale for the scalar
triplet field becomes much larger than the electroweak scale. The requirements
of perturbativity of the couplings and agreement with electroweak data place
strong restrictions on models with Higgs triplets. Our results have important
implications for Little Higgs type models and other models with rho not equal
to one at tree level.Comment: 23 page
