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.

51 pages, 14 figures, 4 tables

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