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 quantized field theory and to construct a low-energy one-loop effective Lagrangian by integrating out the heavy degrees of freedom in the path integral. We apply this method to the Higgs boson in a spontaneously broken SU(2) gauge theory (gauged linear {σ} model). In this context, the background-field method is generalized to the nonlinear representation of the Higgs sector by applying (a generalization of) the Stueckelberg formalism. The (background) gauge-invariant renormalization is discussed. At one loop the lnMH terms of the heavy-Higgs-boson limit of this model coincide with the UV-divergent terms of the corresponding gauged nonlinear {σ} model, but vertex functions differ in addition by finite (constant) terms in both models. These terms are also derived by our method. Diagrammatic calculations of some vertex functions are presented as a consistency check. {} 1995 The American Physical Society.