Exploring the Null Results in the Direct Detection Experiments, $(g-2)_\ell$ and Neutrino Mass in an Extended $U(1)_{L_\mu-L_\tau}$ Model Constrained through the $Z\to\ell^+\ell^-$ Decays

Abstract

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 $U(1)_{L_\mu-L_\tau}$-extension of the Standard Model~(SM) and augmented the particle spectrum with $SU(2)_L$-singlet vector-like leptons and scalars. A discrete $Z_2$ 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 $Z\ell^+\ell^-$ couplings. The experimental bounds on the $Z\to\ell^+\ell^-$ decays are instrumental in constraining the model parameters. Particularly, using the $Z\to\tau^+\tau^-$ decay, a stronger exclusion limit can be imposed on the $U(1)_{L_\mu-L_\tau}$ parameter space. Further, in the presence of three heavy right-handed neutrinos, transforming as $Z_2$-even states, the model can explain all the neutrino mass and mixing constraints using the Type-I seesaw mechanism. Future experimental updates on the $(g-2)_\ell$, $Z\to\ell^+\ell^-$ decays and improved bounds on the $U(1)_{L_\mu-L_\tau}$ 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.