Non-perturbative fixed points and renormalization group improved effective potential

TL;DR

This paper investigates the effects of non-perturbative fixed points on the stability of the effective potential in scalar QED and QCD, revealing how these fixed points influence potential barriers and minima.

Contribution

It introduces the calculation of the effective potential assuming non-perturbative fixed points, extending the understanding of stability conditions in these models.

Findings

In scalar QED, the potential barrier is barely affected near the fixed point.

In QCD with a scalar, the potential barrier and local minimum are significantly altered.

Non-perturbative fixed points impact the shape and stability of the effective potential.

Abstract

The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of non-perturbative fixed points associated to a conformal phase. In the case of scalar QED the barrier of instability found previously is barely displaced as we approach the fixed point, and in the case of QCD with a colorless scalar not only the barrier is changed but the local minimum of the potential is also changed.