A Renormalization Group Flow Approach to Decoupling and Irrelevant Operators

Abstract

Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a φ 4-type scalar field theory involving two real scalar fields (one in heavy with mass M and the other light). Then, to all orders in perturbation theory, it is shown that effects of virtual heavy particles up to the order 1/ M 2 N 0 can be systematically incorporated into light-particle theory via effective local vertices of canonical dimension at most 4 + 2 N 0. The couplings for vertices of dimension 4 + 2 N are of order 1/ M 2 N and are systematically calculable. All this is achieved through intuitive dimensional arguments without resorting to complicated graphical arguments or convergence theorems.