The Z3 soft breaking in the I(2+1)HDM and its cosmological probes

A bstract A Z 3 symmetric 3-Higgs Doublet Model (3HDM) with two inert doublets and one active doublet (which plays the role of the Higgs doublet), the so-called I(2+1)HDM, is studied. We discuss the behaviour of this 3HDM realisation when one allows for a Z 3 soft-breaking term. In this setup, the lightest Z 3 charged neutral scalar can be a Dark Matter (DM) candidate. If the breaking scale is small enough, this model provides a long-lived neutral state with the opposite CP parity to the DM state. This long-lived particle could then be another effective DM candidate when its lifetime is comparable to the age of the universe. In this case, we have studied the properties of the ensuing relic density in the presence of the most recent limits from direct searches for DM. Conversely, the case in which the long-lived particle actually decays into the DM particle and Standard Model particles in a detector at a collider experiment is very attractive from the viewpoint of phenomenology. Under such conditions, we have studied signatures involving missing transverse energy and multiple leptons (and jets) at the International Linear Collider (ILC) in the presence of displaced vertices.