DERIVING NONDECOUPLING EFFECTS OF HEAVY FIELDS FROM THE PATH-INTEGRAL- A HEAVY HIGGS FIELD IN AN SU(2) GAUGE-THEORY

We describe a method to remove nondecoupling heavy fields from a quant ized field theory and to construct a low-energy one-loop effective Lag rangian by integrating out the heavy degrees of freedom in the path in tegral. We apply this method to the Higgs boson in a spontaneously bro ken SU(2) gauge theory (gauged linear sigma model). In this context, t he background-held method is generalized to the nonlinear representati on of the Higgs sector by applying (a generalization of) the Stueckelb erg formalism. The (background) gauge-invariant renormalization is dis cussed. At one loop the In M(H) terms of the heavy-Higgs-boson limit o f this model coincide with the UV-divergent terms of the corresponding gauged nonlinear sigma model but vertex functions differ in addition by finite (constant) terms in both models. These terms are also derive d by our method. Diagrammatic calculations of some vertex functions ar e presented as a consistency check.