The FIMP-WIMP dark matter in the extended singlet scalar model

We explore the simplest viable dark matter model with a real singlet scalar, vector-like singlet and doublet fermions. The Yukawa couplings associated with the fermion sector play a crucial role in getting the current relic density through Freeze-in and Freeze-out mechanism. We discuss the constraints from the recent muon anomalous magnetic moment experimental data and relic density. We also perform the collider analysis for the FIMP dark matter in the context of 14 TeV LHC experiments with the MATHUSLA100/200 detector. Our analysis shows that one can get enough events $>3$ for heavy charged fermion track at 14 TeV LHC with an integrated luminosity $\mathcal{L}={10}^6\mathrm{f}{\mathrm{b}}^{-1}$.