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

Bibhabasu De

TL;DR

This work extends the SM by a leptophilic $U(1)_{L_ ext{μ}-L_ ext{τ}}$ gauge symmetry and a semi-simple field content of vector-like leptons and scalars, stabilized by a $Z_2$ symmetry. The model yields a DM candidate whose DM–SM scattering amplitudes cancel at leading order, explaining the persistent direct-detection null results, while still providing a calculable $Z'$ portal for relic-density and lepton-sector observables. It simultaneously delivers one-loop corrections to $Z o ext{ℓ}^+ ext{ℓ}^-$ and lepton $g-2$, with $Z$-pole decays and neutrino masses constraining the parameter space. The framework remains testable via future lepton-flavor observables, refined $Z$-pole measurements, and potential DM–muon scattering searches, offering a coherent link between dark matter phenomenology and lepton-sector anomalies.

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 $U(1)_{L_μ-L_τ}$-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 $Z\toτ^+τ^-$ decay, a stronger exclusion limit can be imposed on the $U(1)_{L_μ-L_τ}$ 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 $U(1)_{L_μ-L_τ}$ 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.

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

TL;DR

This work extends the SM by a leptophilic gauge symmetry and a semi-simple field content of vector-like leptons and scalars, stabilized by a symmetry. The model yields a DM candidate whose DM–SM scattering amplitudes cancel at leading order, explaining the persistent direct-detection null results, while still providing a calculable portal for relic-density and lepton-sector observables. It simultaneously delivers one-loop corrections to and lepton , with -pole decays and neutrino masses constraining the parameter space. The framework remains testable via future lepton-flavor observables, refined -pole measurements, and potential DM–muon scattering searches, offering a coherent link between dark matter phenomenology and lepton-sector anomalies.

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 -extension of the Standard Model~(SM) and augmented the particle spectrum with -singlet vector-like leptons and scalars. A discrete 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 couplings. The experimental bounds on the decays are instrumental in constraining the model parameters. Particularly, using the decay, a stronger exclusion limit can be imposed on the parameter space. Further, in the presence of three heavy right-handed neutrinos, transforming as -even states, the model can explain all the neutrino mass and mixing constraints using the Type-I seesaw mechanism. Future experimental updates on the , decays and improved bounds on the 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.

Paper Structure

This paper contains 21 sections, 95 equations, 14 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Kinetic Mixing
  3. Fermion Loop
  4. Scalar Loop
  5. The Model
  6. Scalar Sector
  7. Collider Constraints
  8. Existing Bounds on the Minimal $\mathbf{\mathcal{G}_{\rm SM}\otimes U(1)_{L_\mu-L_\tau}}$
  9. Dark Matter Phenomenology
  10. Relic Density
  11. Direct Detection Prospects
  12. New Physics Contributions to $Z\to\ell^+\ell^-$
  13. $\mathbf{Z\to e^+e^-}$
  14. $\mathbf{Z\to\mu^+\mu^-}$
  15. $\mathbf{Z\to\tau^+\tau^-}$
  16. ...and 6 more sections

Figures (14)

  • Figure 1: Kinetic mixing at one-loop level due to a generic fermion $f$ (a) and a scalar $S$ (b, c) with non-zero $X$, $Y$ charges. $B_\mu$ and $Z^\prime_\nu$ are the gauge bosons associated with $U(1)_Y$ and $U(1)_X$, respectively. $q$ defines the transferred momentum.
  • Figure 2: Current constraints on the $U(1)_{L_\mu-L_\tau}$ theory. The grey, blue, red, golden, and violet shaded regions represent the parts of the parameter space excluded through the CCFR CCFR:1991lpl, BBN Escudero:2019gzq, NA64$\mu$NA64:2024klw, BABAR BaBar:2016sci, and LHC ATLAS:2023vxg results, respectively.
  • Figure 3: Possible $s$-channel diagrams contributing to the total annihilation cross section of $\chi_1$. For $m_1>m_\tau$, $f_{\rm SM}\equiv\mu$, $\nu_\mu$, $\tau$, $\nu_\tau$.
  • Figure 4: Variation of $\Omega_1 h^2$ as a function of $m_1$. The colors violet, green, golden, blue, and red correspond to $\left(M_{Z^\prime}=20~{\rm MeV},\, g^\prime=10^{-4}\right)$, $\left(M_{Z^\prime}=200~{\rm MeV},\, g^\prime=3\times 10^{-4}\right)$, $\left(M_{Z^\prime}=2~{\rm GeV},\, g^\prime=10^{-3}\right)$, $\left(M_{Z^\prime}=20~{\rm GeV},\, g^\prime=3\times 10^{-3}\right)$, and $\left(M_{Z^\prime}=200~{\rm GeV},\, g^\prime=0.1\right)$, respectively. For a given $g^\prime$, $\rho_1=10g^\prime$. The black line represents the observed DM abundance from the Planck Planck:2018vyg.
  • Figure 5: Variation of $\bar{\sigma}_{\chi_1\mu}$ as a function of the DM mass $m_1$ for $(g^\prime/M_{Z^\prime})\in\,[10^{-7},\,1]$ GeV$^{-1}$.
  • ...and 9 more figures