Non-triviality of gauge theories with elementary scalars and upper bounds on Higgs masses

Abstract

Strong evidence supports the idea that pure φ 4 field theory is trivial (non-interacting) in four dimensions. In the context of perturbation theory when gauge fields or fermions are present the combined theory may become non-trivial for a limited range of values of the renormalized coupling constants. Calculable upper bounds on the masses of elementary Higgs particles are implied by the restrictions on these coupling constants. Other constraints (on, e.g. the number of fermions in the theory) are also implied.