Seesaw lepton masses and muon $$g-2$$ from heavy vector-like leptons

We propose a model for the vector-like lepton to explain small muon mass by seesaw mechanism, based on lepton-specific two Higgs doublet models with local $$U(1)'$$ symmetry. There is no bare nonzero charge of leptophilic doublet, so physical generated due mixing between and after dark get VEVs. In this scenario, non-decoupling effects give rise leading contributions $$g-2$$ , thanks light $$Z'$$ boson. discuss various constraints from flavor violation, electroweak precision data, as well collider searches.