Singlet-Doublet dark matter freeze-in: LHC displaced signatures versus cosmology

We study the Singlet-Doublet dark matter model in the regime of feeble couplings, where the dark matter abundance is obtained via the freeze-in mechanism. As a consequence of the small couplings, the heavier particles in the model are long-lived with decay length at typical scales of collider experiments. We analyse the collider signatures of the model, characterised by displaced h and Z bosons plus missing momentum, employing current LHC searches for displaced vertices and missing energy to significantly constrain the parameter space of the model. We also take into account the cosmological bounds relevant for our light dark matter candidate arising from Lyman-α forest constraints. Our analysis emphasises the interplay between displaced signatures at the LHC and cosmology for dark matter candidates whose relic abundance is obtained through the freeze-in mechanism.