Sensitivity of the FACET experiment to Heavy Neutral Leptons and Dark Scalars

We analyze the potential of the recently proposed experiment FACET (Forward-Aperture CMS ExTension) to search for new physics. As an example, we consider the models of Higgs-like scalars with cubic and quartic interactions and Heavy Neutral Leptons. We compare the sensitivity of FACET with that of other proposed "intensity frontier" experiments, including FASER2, SHiP, etc. and demonstrate that FACET could probe an interesting parameter space between the current constraints and the potential reach of the above mentioned proposals.