Proof of the decoupling theorem of field theory in Minkowski space. II. Theories involving particles with vanishingly small masses

Abstract

The decoupling theorem of quantum field theory is studied in Minkowski space for theories which on experimental grounds may contain particles with vanishingly small masses. Rules are set up to prove the distributional vanishing property of the renormalized amplitudes when any subset of the underlying masses is scaled to infinity, and any subset of the remaining masses is scaled to zero. By careful estimates, the analysis in Minkowski space may be reduced to a similar one in Euclidean space. All subtractions of renormalization are carried out at the origin of momentum space with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram.