Spontaneous breaking of vector symmetries and the non-decoupling light Higgs particle

Abstract

Using a four fermion interaction Lagrangian, we demonstrate that the spontaneous breaking of vector symmetries requires the existence of a light (comparing with the heavy fermion mass) scalar particle and the low energy effective theory (the $\sigma$ model) obtained after integrating out heavy fermion degrees of freedom is asymptotically a renormalizable one. When applying the idea to the electroweak symmetry breaking sector of the standard model, the Higgs particle's mass is of the order of the electroweak scale: $185GeV/\sqrt{N_c}<m_H<720GeV/\sqrt{N_c}$ where $N_c$ is the color degrees of freedom of the heavy fermion fields.

Comments: 8 pages, Latex.