On the decoupling theorem in field theory

Abstract

An elementary proof of the decoupling theorem in field theory is given when all the masses in the theory are allowed to go to infinity. The proof is given directly in momentum space with the subtractions of the theory performed at the origin and containing nonzero mass particles. The theorem states that, in Euclidean space, if the masses of the theory are scaled by l and l is allowed to go to infinity then the corresponding Feynman amplitude vanishes not more slowly than l−1, i.e., ‖ 𝒜‖<l−1C, for l⩾1.