The Direct Detection (DD) experiments are vital for probing the particle nature of Dark Matter (DM). However, in the absence of a scattering event, DD searches result in stringent bounds on the corresponding parameter space. The paper has considered a \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) -extension of the Standard Model (SM) and augmented the particle spectrum with SU(2)L-singlet vector-like leptons and scalars. A discrete Z2 symmetry stabilizes the lightest SM-singlet vector-like lepton as the viable DM candidate. In the proposed model, amplitude-level cancellation can be achieved for both DM-electron and DM-quark scatterings, leading to a trivial explanation for the continuous null results in the DD experiments. The framework can also induce one-loop corrections to the lepton anomalous magnetic moments and Zℓ+ℓ− couplings. The experimental bounds on the Z → ℓ+ℓ− decays are instrumental in constraining the model parameters. Particularly, using the Z → τ +τ − decay, a stronger exclusion limit can be imposed on the \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) parameter space. Further, in the presence of three heavy right-handed neutrinos, transforming as Z2-even states, the model can explain all the neutrino mass and mixing constraints using the Type-I seesaw mechanism. Future experimental updates on the (g − 2)ℓ, Z → ℓ+ℓ− decays and improved bounds on the \( \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} \) theory can be crucial to test the proposed model. Moreover, future DD experiments searching for a DM-muon scattering might be significant to probe the considered DM-SM interaction.
