FIMP dark matter freeze-in gauge mediation and hidden sector

We explore the dark matter freeze-in mechanism within the gauge mediation framework, which involves a hidden feebly interacting massive particle (FIMP) coupling feebly with the messenger fields while the messengers are still in the thermal bath. The FIMP is the fermionic component of the pseudo-moduli in a generic metastable supersymmetry (SUSY) breaking model and resides in the hidden sector. The relic abundance and the mass of the FIMP are determined by the SUSY breaking scale and the feeble coupling. The gravitino, which is the canonical dark matter candidate in the gauge mediation framework, contributes to the dark matter relic abundance along with the freeze-in of the FIMP. The hidden sector thus becomes two-component with both the FIMP and gravitino lodging in the SUSY breaking hidden sector. We point out that the ratio between the FIMP and the gravitino is determined by how SUSY breaking is communicated to the messengers. In particular when the FIMP dominates the hidden sector, the gravitino becomes the minor contributor in the hidden sector. Meanwhile, the neutralino is assumed to be both the weakly interacting massive particle dark matter candidate in the freeze-out mechanism and the lightest observable SUSY particle. We further find out the neutralino has the sub-leading contribution to the current dark matter relic density in the parameter space of our freeze-in gauge mediation model. Our result links the SUSY breaking scale in the gauge mediation framework with the FIMP freeze-in production rate leading to a natural and predicting scenario for the studies of the dark matter in the hidden sector.