Exploring the Null Results in the Direct Detection Experiments and the (g-2)_ in an Extended U(1)L_μ-L_τ Model Constrained through the Z→⁺⁻ Decays

The Direct Detection (DD) experiments are vital for probing the particle nature of the 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 U(1)L_μ-L_τ-extension of the Standard Model (SM) and augmented the particle spectrum with SU(2)L-singlet vector-like leptons and scalars. Further, 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 Z⁺⁻ couplings. The experimental bounds on the Z→⁺⁻ decays are instrumental in constraining the model parameters. Particularly, using the Z→τ⁺τ⁻ decay, a stronger exclusion limit can be imposed on the U(1)L_μ-L_τ parameter space. Future experimental updates on the (g-2)_, Z→⁺⁻ decays and improved bounds on the U(1)L_μ-L_τ 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.