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 ${\varphi }^4$-type scalar field theory involving two real scalar fields (one is 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 $1/M^{2N_0}$ can be systematically incorporated into light-particle theory via effective local vertices of canonical dimension at most $4+2N_0$. The couplings for vertices of dimension $4+2N$ are of order $1/M^{2N}$ and are systematically calculable. All this is achieved through intuitive dimensional arguments without resorting to complicated graphical arguments or convergence theorems.

Comments: 26 pages, LaTeX, 1 figure Revised version to appear in Annals of Physics (Title was changed. Renormalization conditions on heavy fields were changed to physical ones.)