Renormalization group running of the minimal leptophilic dark matter model toward a UV completion

We study the renormalization group running of the coupling constants in a minimal leptophilic dark matter model in which a Standard Model singlet fermion, acting as the dark matter (DM) candidate, couples exclusively to right-handed charged leptons via a new charged scalar mediator. Reproduction of the observed thermal relic abundance of the DM candidate requires sizable Yukawa couplings, and such sizable Yukawa couplings can significantly affect the renormalization group evolution of the model parameters. We examine the conditions that the model remains perturbative and the vacuum stability is maintained up to high-energy scales. We find that the parameter space is severely constrained to ensure the perturbativity and the vacuum stability up to the Planck scale. In particular, the masses of the dark matter and the charged scalar mediator should be smaller than about 350 GeV and can be tested by future collider experiments. The lower bound of the dark matter mass that is larger than a few GeV is also obtained by perturbativity.