Lepton portal dark matter at muon colliders: Total rates and generic features for phenomenologically viable scenarios

Lepton portal dark matter (DM) models are a class of models where the DM candidates solely couple to charged leptons through a mediator carrying a lepton number. These models are very interesting since they avoid constraints from direct detection experiments even for coupling of order ${\cal O}(1)$, they have small annihilation cross sections, and can be probed efficiently at lepton colliders. In this work, we consider a minimal lepton portal DM model which consists of extending the SM with two $SU(2)_L$ singlets: a charged scalar singlet and an electrically neutral right-handed fermion. We systematically study the production mechanisms of DM at multi-TeV muon colliders. After considering all the possible theoretical and experimental constraints and studying the phenomenology of lepton flavour violation and DM in the muon-philic scenario, we analyse the production rates of 54 channels (26 channels for prompt DM production and 28 channels for charged scalar production) at multi-TeV muon colliders. Finally, we discuss the possible collider signatures of some channels and the corresponding backgrounds. We find that at least 9 channels for DM production can be very efficient in testing DM with masses up to about $1$ TeV.