Fermion-Portal Dark Matter at a High-Energy Muon Collider

In this work, we provide a comprehensive study of fermion-portal dark matter models in the freeze-in regime at a future muon collider. For different possible non-singlet fermion portals, we calculate the upper bound on the mediator's mass arising from the relic abundance calculation and discuss the reach of a future muon collider in probing their viable parameter space in prompt and long-lived particle search strategies. In particular, we develop rudimentary search strategies in the prompt region and show that cuts on the invariant dilepton or dijet masses, the missing transverse mass $M_{T2}$, pseudorapidity and energy of leptons or jets, and the opening angle between the lepton or the jet pair can be employed to subtract the Standard Model background. In the long-lived particle regime, we discuss the signals of each model and calculate their event counts. In this region, the lepton-(quark-)portal model signal consists of charged tracks ($R$-hadrons) that either decay in the detector to give rise to a displaced lepton (jet) signature, or are detector stable and give rise to heavy stable charged track signals. As a byproduct, a pipeline is developed for including the non-trivial parton distribution function of a muon component inside a muon beam; it is shown that this leads to non-trivial effects on the kinematic distributions and attainable significances. We also highlight phenomenological features of all models unique to a muon collider and hope our results, for this motivated and broad class of dark matter models, inform the design of a future muon collider detector. We also speculate on suggestions for improving the sensitivity of a muon collider detector to long-lived particle signals in fermion-portal models.