Multi-scale Renormalization

TL;DR

This paper proposes a two-scale renormalization group approach to better handle multi-scale problems in quantum field theory, specifically improving the computation of the effective potential in the Higgs-Yukawa model.

Contribution

It introduces a modified two-scale renormalization scheme with a resummation method for large logarithms in beta functions, enhancing perturbative calculations for multi-scale systems.

Findings

Developed a two-scale RG scheme for multi-scale problems.

Derived a resummation technique for large logarithms in beta functions.

Applied the method to the Higgs-Yukawa model's effective potential.

Abstract

The Standard MS renormalization prescription is inadequate for dealing with multi-scale problems. To illustrate this we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that it is natural to employ a two-scale renormalization group. We give a modified version of a two-scale scheme introduced by Einhorn and Jones. In such schemes the beta functions necessarily contain potentially large logarithms of the RG scale ratios. For credible perturbation theory one must implement a large logarithms resumation on the beta functions themselves. We show how the integrability condition for the two RG equations allows one to perform this resummation.