Multiscale Renormalization and Decoupling

TL;DR

This paper discusses the limitations of standard multiscale renormalization in complex problems and proposes a two-scale renormalization group approach, exemplified through the Higgs-Yukawa model, to better handle multiscale issues.

Contribution

It introduces a two-scale renormalization group method to improve multiscale problem handling in quantum field theories, especially regarding heavy particle decoupling.

Findings

Standard MS renormalization is inadequate for multiscale problems.

A two-scale renormalization group approach is proposed and reviewed.

The approach better aligns with heavy particle decoupling principles.

Abstract

The standard MS renormalization prescription is inadequate for dealing with multiscale problems. To illustrate this, we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that the most natural way to deal with this problem is to introduce a 2-scale renormalization group. We review various ways of implementing this idea and consider to what extent they fit in with the notion of heavy particle decoupling.