THE DECOUPLING THEOREM IN EFFECTIVE SCALAR FIELD-THEORY

We consider decoupling in the context of an effective quantum field th eory of two scalar fields with well separated mass scales and a Z(2) x Z(2) symmetry. We first prove, using Wilson's exact renormalization g roup equation, that the theory is renormalizable, in the same way that we showed in a previous paper that theories with a single mass scale were renormalizable. We then state and prove a decoupling theorem: at scales below the mass of the heavy particle the full theory may be app roximated arbitrarily closely by an effective theory of the light part icle alone, with naturalness scale the heavy particle mass. We also co mpare our formulation of effective field theory with the more conventi onal local formulation. (C) 1995 Academic Press, Inc.