Generalized decoupling theorem in quantum field theory

Abstract

Previous analyses of the decoupling theorem, in Euclidean space, considered only one mass scale in the theory becoming large and had the stringent constraint of allowing no zero mass particles in the theory. We generalize the decoupling theorem in both respects. We prove the vanishing property of renormalized Feynman amplitudes, with subtractions, when any subset of the masses in the theory become large and, in general, at different rates, thus providing different large mass scales in the theory. This theorem is then extended and we give sufficiency conditions for the validity of the decoupling theorem when any subset of the remaining nonasymptotic masses are scaled to zero and, in general, at different rates. All the subtractions of renormalization are carried out at the origin of momentum space. The proof applies for theories with derivative couplings and with higher spin fields as well.