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

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.