Consistent Conformal Extensions of the Standard Model

TL;DR

This paper examines the consistency of classically conformal extensions of the standard model with experimental data, contrasting different scalar-gauge coupling hierarchies and their phenomenological implications.

Contribution

It compares two hierarchy assumptions for scalar and gauge couplings in conformal standard model extensions and analyzes their impact on phenomenological predictions.

Findings

Different coupling hierarchies lead to distinct phenomenological outcomes.

The Gildener-Weinberg approach assumes scalar couplings scale as g^2, while recent arguments suggest g^4.

The choice of hierarchy affects the model's experimental viability.

Abstract

The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multi-scalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy $\lambda_\text{s} \sim g^2_\text{g}$ of scalar and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently argued that in the (single-scalar) standard model, gauge invariant results require the consistent scaling $\lambda_\text{s} \sim g^4_\text{g}$. In the present paper we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.