Meanfield Study of Radially Active U(1) and SU(2) Higgs Model

The phase structure of lattice Higgs model has been studied by many authorsl)-4) with radial excitations of the Higgs scalar frozen out. Revealed was a remarkable feature of complementarityl),5) which states that, in Higgs models with a scalar in the fundamental representation, the Higgs and the confining phases are analytically connected with each other. Many applications of the complementarity have been made in the continuum theory.6) However the continuum limit of lattice models is expected to be attained for renormalizable interactions,7) whereas the frozen Higgs models are not renormalizable. It will thus be necessary to study radially active models and clarify their phase structures. Many approaches are possible; Monte Carlo simulations and analytic studies. Among the latters the meanfield (MF) theory is very useful since it has succeeded in reproducing phase diagrams qualitatively and enables us to calculate further corrections systematically.3) Recently Munehisa and Munehisa) have performed a Monte Carlo study of a radially active Z2 lattice Higgs model using a discrete approximation of the radial mode r. In the previous paper) we made a series of MF studies of this model and showed that the MF theory was qualitatively successful also in the radially active model as in the frozen model. 4) We also discussed that the concept of a mode correlation is useful to understand the physical properties of each MF model. In this paper we extend the previous analysis to more realistic Higgs models of U(1) and SU(2) gauge groups. In §2 we first introduce the models and give a brief review of MF method in a suitable manner for application to our models. We then investigate the U(1) and SU(2) Higgs models in §§3 and 4. Section 5 is devoted to the conclusion and discussion.