We consider the mixed WIMP-FIMP scenario in a two-component dark matter model with Z₂ Z₄ symmetry, where a singlet scalar S and a Majarano fermion χ are introduced as dark matter candidates. We also introduce another singlet scalar S₀ with a non-zero vacuum expectation value to the SM so that the fermion dark matter can obtain mass after spontaneous symmetry breaking. Either S or χ relic density can be generated via the "Freeze-out" mechanism. In contrast, the other DM candidate relic density is obtained by the "Freeze-in" mechanism, and we therefore have two different cases. In the case of χ as WIMP and S as FIMP, we perform random scans to estimate the allowed parameter space consistent with the dark matter constraint. The results show that this case is viable over a wide range of dark matter masses with the Yukawa coupling of S₀ and χ should be larger than 1. Instead, for the case of S as WIMP and χ as FIMP, the viable parameter space is more constrained by the direct detection experiements, and we have two regions with mS 62. 5 GeV and mS>400 GeV under the constraints, which is consistent with the singlet scalar DM result but the scalar DM mass can be as low as a few hundred GeV for the heavy mass region in the model.
Qi et al. (Mon,) studied this question.