Perspective of inert quartet in the context of perturbativity and dark matter phenomenology
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 $β$-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.