  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: $185
GeV /\sqrt{N_c} < m_H < 720 GeV /\sqrt{N_c}$ where $N_c$ is the color degrees
of freedom of the heavy fermion fields.
