The Minimal Axion Minimal Linear $\sigma$ Model

TL;DR

This paper extends the minimal linear sigma model with an extra scalar to generate axions or axion-like particles, analyzing their phenomenology and potential detection in collider experiments.

Contribution

It introduces a new minimal scenario within the $SO(5)/SO(4)$ model that incorporates axion physics and studies its scalar potential and phenomenological implications.

Findings

Identifies a minimal scalar potential consistent with symmetry breaking.

Shows two possible axion scenarios: QCD axion and axion-like particle.

Analyzes phenomenological features of scalar and fermionic sectors.

Abstract

The minimal $SO(5)/SO(4)$ linear $\sigma$ model is extended including an additional complex scalar field, singlet under the global $SO(5)$ and the Standard Model gauge symmetries. The presence of this scalar field creates the conditions to generate an axion \`a la KSVZ, providing a solution to the strong CP problem, or an axion-like-particle. Different choices for the PQ charges are possible and lead to physically distinct Lagrangians. The internal consistency of each model necessarily requires the study of the scalar potential describing the $SO(5)\to SO(4)$, electroweak and PQ symmetry breaking. A single minimal scenario is identified and the associated scalar potential is minimised including counterterms needed to ensure one-loop renormalizability. In the allowed parameter space, phenomenological features of the scalar degrees of freedom, of the exotic fermions and of the axion are illustrated. Two distinct possibilities for the axion arise: either it is a QCD axion with an associated scale larger than $\sim10^{5}$ TeV and therefore falling in the category of the invisible axions; or it is a more massive axion-like-particle, such as a $1$ GeV axion with an associated scale of $\sim200$ TeV, that may show up in collider searches.