On the scale hierarchy in radiative symmetry breaking

TL;DR

This paper investigates how a hierarchy of scales emerges in radiative symmetry breaking within a simple quantum field theory, using the Coleman-Weinberg mechanism to analyze the effective potential and its implications.

Contribution

It demonstrates the emergence of a scale hierarchy in radiative symmetry breaking and constructs an effective model near the potential minimum, clarifying the infrared applicability limits.

Findings

Hierarchy between renormalization scale and scalar VEV established

Effective model parameters determine the infrared applicability limit

Absence of direct RG transition to the original theory confirmed

Abstract

The emergence of a scale hierarchy in the case of spontaneous radiative breaking of conformal symmetry is discussed using the example of a simple quantum field theory model. The Coleman-Weinberg mechanism is implemented in the one-loop approximation of the effective potential of a scalar field interacting with a fermion field. The emergence of a hierarchy between the renormalization scale and the magnitude of the scalar field vacuum expectation value is shown. An effective model in the vicinity of the effective potential minimum is constructed, and absence of a direct renormalization group transition to the original theory is established. It is shown that effective model parameters measurement in the infrared region allows us to determine the scale that limits the applicability region of the model.