A RENORMALIZATION-GROUP ANALYSIS OF THE HIGGS-BOSON WITH HEAVY FERMIONS AND COMPOSITENESS

We study the properties of heavy fermions in the vector-like represent ation of the electro-weak gauge group SU(2)(w) x U(1)(Y) with Yukawa c ouplings to the standard model Higgs boson. Using the renormalization group analysis, we discuss their effects on the vacuum stability and t he triviality bound on the Higgs self-coupling, within the context of the standard model (i.e., the Higgs particle is elementary). Contrary to the low energy case where the decoupling theorem dictates their beh avior, the inclusion of heavy fermions drastically changes the standar d model structure at high scales. We also discuss the interesting poss ibility of compositeness, i.e., the Higgs particle is composed of the heavy fermions using the method of Bardeen, Hill and Lindner [Phys. Re v. D 41 (1990) 1647]. Finally we briefly comment on their possible rol e in explaining R(b) and R(c).