Inert dark matter in three Higgs doublet model: a blind spot narrative

Abstract: We explore the phenomenology of three Higgs doublet scenario, where the scalar potential is augmented by $\mathbb{Z}{3} \times \mathbb{Z}{2}$ symmetry making one doublet inert. Thus in effect, our model of interest is two Higgs plus inert Higgs doublet model charged under $\mathbb{Z}_3$ ((2+I)HDM-$\mathbb{Z}_3$) symmetry. We observe a blind spot feature for dark matter direct detection, as the tree-level dark matter-nucleon scattering cross-section vanishes depending on the mass splitting of dark sector particles. We perform a detailed analysis based on vacuum stability, unitarity, relic abundance, and direct detection results on the model. We also perform profile likelihood analysis and constrain the corresponding parameter space.