Obscure Higgs boson at Colliders

In this study we consider an extension of the Standard Model with a complex hypercharge zero triplet scalar. In this scenario one of the charged Higgs bosons remains purely triplet and does not couple to the fermions, making it elusive at colliders. Also the physical pseudoscalar is a pure triplet and this purity makes it a suitable dark matter candidate without the need of discrete symmetries, unlike other extensions. The bounds from relic density and direct dark matter search experiments select its mass to be $\sim 1.35-1.60$ TeV. The pure triplet charged Higgs gives rise to displaced signatures and their sensitivity at LHC and MATHUSLA have been studied. The prospects at present and future hadron/muon colliders of such exotic scalars are pointed out by calculating their productions cross-section and dominant decay modes. We present also the expected reach for the triplet states at a multi-TeV muon collider.