Renormalization Group and Effective Potential in Classically Conformal Theories

TL;DR

This paper derives a general RG improved effective potential formula for classically conformal theories, demonstrating its application to models including QCD with scalar fields, revealing insights into stability, symmetry breaking, and potential links to electroweak scale.

Contribution

The authors provide a closed-form RG improved effective potential formula for conformal models, enabling analysis of stability and symmetry breaking with new insights into IR barriers and QCD-electroweak connections.

Findings

Convexity of the effective potential is restored by RG improvement.

Infrared barrier $\Lambda_{IR}$ indicates unavoidable symmetry breaking.

Potential links between $\Lambda_{QCD}$ and electroweak scale are suggested.

Abstract

We derive a general formula for the RG improved effective (Coleman-Weinberg) potential for classically conformal models, applying it to several examples of physical interest, and in particular a model of QCD coupled via quarks to a colorless scalar field. The closed form expressions allow us to discuss the range of validity of the effective potential as well as the issue of `large logarithms' in a way different from previous such analyses. Remarkably, in all examples considered, convexity of the effective potential is restored by the RG improvement, or otherwise the potential becomes unstable. In the former case, symmetry breaking becomes unavoidable due to the appearance of an infrared barrier $\Lambda_{IR}$, which hints at a so far unsuspected link between $\Lambda_{QCD}$ and the scale of electroweak symmetry breaking.