The Decoupling Theorem in Effective Scalar Field Theory

TL;DR

This paper proves a decoupling theorem for a two-scalar field effective theory, showing that below the heavy particle's mass scale, the theory simplifies to an effective theory of the light particle, with renormalizability established via Wilson's RG.

Contribution

It provides a rigorous proof of decoupling in a two-scalar effective field theory using Wilson's exact renormalization group, extending previous single-scale renormalizability results.

Findings

Decoupling holds below the heavy particle mass scale.

The full theory can be approximated by an effective light-particle theory.

The formulation aligns with conventional effective field theory approaches.

Abstract

We consider decoupling in the context of an effective quantum field theory of two scalar fields with well separated mass scales and a $Z_2\times Z_2$ symmetry. We first prove, using Wilson's exact renormalization group equation, that the theory is renormalizable, in the same way that we showed in a previous paper that theories with a single mass scale were renormalizable. We then state and prove a decoupling theorem: at scales below the mass of the heavy particle the full theory may be approximated arbitrarily closely by an effective theory of the light particle alone, with naturalness scale the heavy particle mass. We also compare our formulation of effective field theory with the more conventional local formulation.