A Renormalization Group Analysis of the Higgs Boson with Heavy Fermions and Compositeness

We study the properties of heavy fermions in the vector-like representation of the electro-weak gauge group SU(2)W × U(1)Y with Yukawa couplings to the standard model Higgs boson. Using the renormalization group analysis, we discuss their effects on the vacuum stability and the 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 behavior, the inclusion of heavy fermions drastically changes the standard model structure at high scales. We also discuss the interesting possibility of compositeness, i.e., the Higgs particle is composed of the heavy fermions using the method of Bardeen, Hill and Lindner [1]. Finally we briefly comment on their possible role in explaining Rb and Rc. †) e-mail address: [email protected] Enormous efforts have been made in searching for physics beyond the standard model but up to now a crucial, direct experimental indication is still illusive. One of the most important motivation to explore heavy fermions above the energy accessible by current accelerators is to look for extra building blocks of nature beyond the three families of the standard model. For this purpose it may be adequate to look at fermions in vector-like representations of the electro-weak gauge group with a large bare mass term, rather than the conventional chiral doublets. The main reason for this is from the strong experimental constraint on the S parameter [2]. While the experiments favour a negative value of S [3], a standard chiral doublet of heavy fermions (degenerate in mass) contributes to the S parameter as 1/6π. On the contrary, for fermions in the vector-like representation of the electro-weak gauge group a large bare fermion mass M completely changes the low energy properties of the heavy fermions. As a consequence of the decoupling theorem, heavy fermions contribute to the S and T parameters as,