  We consider decoupling in the context of an effective quantum field theory of
two scalar fields with well separated mass scales and a $Z_2\times Z_2$
symmetry. We first prove, using Wilson's exact renormalization group 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 approximated arbitrarily closely by an effective theory
of the light particle alone, with naturalness scale the heavy particle mass. We
also compare our formulation of effective field theory with the more
conventional local formulation.
