A Renormalization Group Flow Approach to Decoupling and Irrelevant Operators

TL;DR

This paper presents a new proof of decoupling in scalar field theories using Wilson-Polchinski renormalization group equations, demonstrating systematic incorporation of heavy particle effects into effective light-particle theories through local vertices.

Contribution

It introduces a simple, intuitive method to analyze decoupling and irrelevant operators in scalar field theories using renormalization group flow without complex graphical or convergence arguments.

Findings

Decoupling is proven using Wilson-Polchinski RG equations.

Heavy particle effects can be systematically included via local vertices.

Couplings of vertices are calculable and decrease with increasing mass scale.

Abstract

Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $\phi^4$-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.