Classical Dimensional Transmutation and Renormalization in Massive lambda phi^4 Model

TL;DR

This paper explores the classical renormalization group structure and dimensional transmutation in a massive lambda phi^4 model, revealing that the mass influences the scale but preserves the flow characteristics of the massless case.

Contribution

It extends previous work on massless models by analyzing the effects of mass on classical renormalization and demonstrates the similarity of the beta function to the massless case with specific corrections.

Findings

Classical beta function matches massless case up to IR/UV cutoff ratio corrections.

Dynamically generated scale in massive theory exceeds that in massless theory.

Mass term causes screening, affecting the scale of the theory.

Abstract

Recently, Dvali, Gomez, and Mukhanov have investigated a classical lambda phi^4 model with external source and without mass and they have clarified that there are underlying renormalization group structure, including the phenomenon of the dimensional transmutation, at purely classical level. Especially when the coupling lambda is negative, the classical beta function shows the property of asymptotic freedom as in QCD. In this paper, we investigate the lambda phi^4 model with mass, and clarify the role of the mass. The obtained classical beta function is identical with that of the massless lambda phi^4 model up to the corrections of the ratio of the IR cutoff to UV cutoff, and describes the renormalization flow same as the massless theory. We also found that the dynamically generated scale of massive theory is larger than that of massless theory, which could be due to the screening effect of the mass term.