Perspective of inert quartet in the context of perturbativity and dark matter phenomenology

TL;DR

This paper explores an inert $SU(2)$ quartet extension of the Standard Model, analyzing its perturbativity, fixed points, and dark matter phenomenology, including relic density and detection constraints, with potential for heavy dark matter candidates.

Contribution

It introduces a $ ext{Z}_2$-odd $SU(2)$ quartet model, investigates its fixed points and Landau poles, and studies its dark matter properties beyond 15 TeV mass.

Findings

Dark matter mass can exceed 15 TeV without relic overproduction

Fixed points depend on portal and self-couplings with residual phases

Next-to-lightest particles can be charged or neutral scalars

Abstract

In this article we consider a $\mathbb{Z}_2$-odd $SU(2)$ quartet with hypercharge $Y = +\frac{1}{2}$ as an extension of the Standard Model whose scalar potential which introduces three additional Higgs portal and two self-couplings. We first investigate the possibility of having Landau poles (LPs) in one-loop and Fixed Points (FPs) in two-loop $\beta$-functions of the Higgs quartic couplings. The role of portal and self-couplings with and without residual phases is extensively investigated in obtaining the Fixed Point at two-loop. The model also can provide us with $\mathbb{Z}_2$-odd neutral scalar as the possible dark matter. However not always the lightest state corresponds to the neutral states, and we look into one-loop mass correction for an enhanced dark matter parameter space. This also gives rise to interesting phenomenology of the next-to-lightest particle which can be singly charged, doubly charged or neutral scalar. We performed a detailed study of dark matter relic calculation with one-loop masses and with direct detection bounds, and found out that, unlike the minimal inert extensions of $SU(2)$ multiplets, here the dark matter mass can go beyond 15 TeV without crossing the observed relic. Finally, we summarized with a few benchmark points for future studies.