Freeze-in and Freeze-out of Dark Matter with Charged Long-lived Partners

We present a novel framework capable of addressing the dark matter problem through freeze-in and freeze-out mechanisms, separately or together, depending on the region of the parameter space considered. In the dark matter dynamics, the model features an interplay of thermal production along with sizeable contribution through feeble decay of associated dark fermionic partner, which finally freezes out to the right relic density for a wide range of masses and couplings. Apart from the fermionic dark matter candidate, the model introduces two charged partners, one fermionic and another scalar, which often have delayed decays leading to distinct characteristics of such long-lived particles (LLP) in the colliders like the LHC. Our analysis shows that within the present scenario, LLP of decay length that could be probed at the LHC experiments are compatible with dark matter masses ranging from a few GeV to close to a TeV, as opposed to the requirement of keV-MeV dark matter in simple FIMP scenarios with LLP. In addition, the model presents hitherto unexplored interesting possibilities in the LLP searches, like (i) LLP to LLP to SM cascade decays, which could be searched for within the LHC detectors and (ii) heavy neutral particle decaying within MATHUSLA with two jets and large missing energy. A supplementary aspect of the model is the presence of a heavy neutrino facilitating Type-I seesaw mechanism without disturbing the dark matter side.