Exploring the null results in the direct detection experiments, (g − 2)ℓ and neutrino mass in an extended $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ model constrained through the Z → ℓ+ℓ− decays

A bstract 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 $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>U</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> -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 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 $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>U</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> 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) ℓ , Z → ℓ + ℓ − decays and improved bounds on the $$ \textrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>U</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> </mml:msub> </mml:math> 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.