FIMPs in a two-component dark matter model with $Z_2 \times Z_4$ symmetry

We consider the FIMPs scenario in a two-component dark matter model with $Z_2 \times Z_4$ symmetry, where a singlet scalar $S$ and a Majorana fermion $\chi$ are introduced as dark matter candidates. We also introduce another singlet scalar $S_0$ with a non-zero vacuum expectation value to the SM so that the fermion dark matter can obtain mass after spontaneous symmetry breaking. The model admits six free parameters in the decoupling limit: three masses and three dimensionless parameters. Depending on the mass hierarchies between dark matter particles with half of the new Higgs mass, the DM relic density will be determined by different channels, where $\chi$ and $S$ production can be generated individually. We numerically study the relic density as a function of the model's free parameters and determine the regions consistent with the dark matter constraint for four possible cases. Our results show that this scenario is viable over a wide range of couplings and dark matter masses, where the coupling $\lambda_{ds}$ can be as tiny as $\mathcal{O}(10^{-20})$ level. We stress that even for such tiny couplings, the new Higgs can still play a dominant role in determining dark matter production.