Decoupling theorems for effective field theories

Abstract

This paper continues the program of considering effective field theories which describe a given subset of fields of a quantum field theory. It is shown that predictions of the complete theory, renormalized by means of dimensional regularization with nonminimal subtraction, coincide with those of the local effective field theory with dimension at most four, renormalized by dimensional regularization and minimal subtraction. It is also shown that the renormalization-group equations for low-momenta light-particle processes, as described by the complete theory and the local effective field theory, are identical-a nontrivial result requiring cancellations between the implicit and explicit mass-scale dependence of the parameters of the effective field theory. These results provide the justification for the treatment of the effective field theory as a local theory, uncoupled from the heavy-particle sector. We will present our results in the context of scalar theories with broken symmetry since, for these theories, the demonstration of uncoupling involves the greatest subtlety.