Scalar-Composite Model in 6 - 2\epsilon Dimensions

TL;DR

This paper investigates a scalar composite model in 6-2 epsilon dimensions, demonstrating how quantum effects induce a composite scalar field and analyzing its scale dependence and properties.

Contribution

It establishes the equivalence between a composite scalar model and a renormalizable three-elementary-scalar model under the compositeness condition, revealing scale independence of the coupling.

Findings

The composite scalar coupling is scale-independent.

Quantum effects induce the composite scalar via vacuum polarization.

The model's properties align with previously known general behaviors.

Abstract

We study the model of a composite-scalar made of a pair of scalar fields in 6-2 epsilon dimensions, using equivalence to the renormalizable three-elementary-scalar model under the "compositeness condition." In this model, the composite-scalar field is induced by the quantum effects through the vacuum polarization of elementary-scalar fields with 2N species. We first investigate scale dependences of the coupling constant and masses, in the renormalizable three-elementary-scalar model, and derive the results for the composite model by imposing the compositeness condition. The model exhibits the formerly found general property that the coupling constant of the composite field is independent of the scale.