[Paper Review] Muon g-2 in Lepton Portal Dark Matter

Y. Bai, J. Berger|arXiv (Cornell University)|Apr 7, 2021

Particle physics theoretical and experimental studies34 references17 citations

TL;DR

This paper proposes a lepton portal dark matter model with a real scalar dark matter particle and a charged fermionic mediator, where a large number of internal degrees of freedom ($n_f \approx 30$) suppresses indirect detection signals while enabling the model to explain the observed $4.2\sigma$ excess in the muon anomalous magnetic moment $(g-2)_\mu$. The scenario remains consistent with relic abundance, direct detection, and collider constraints, with dark matter and mediator masses below 200 GeV.

ABSTRACT

The Lepton Portal Dark Matter model, in which dark matter states only coupling to the charged leptons, can explain the excess of the muon anomalous magnetic moment measured by the Muon $g - 2$ experiment. In this paper, we demonstrate that real, charge-neutral scalar dark matter with a large number of internal degrees of freedom and a mass approximately degenerate with the charged fermionic mediator state can accommodate the $(g - 2)_μ$ excess. The model remains consistent with the dark matter relic abundance, direct detection, and indirect detection constraints. The dark matter and its charged fermion partner masses are constrained to be below around 200 GeV. The high-luminosity LHC and future lepton colliders, as well as indirect searches at CTA and GAMMA-400, can test this scenario.

Motivation & Objective

• To explain the $4.2\sigma$ discrepancy in the muon anomalous magnetic moment $(g-2)_\mu$ using a renormalizable model beyond the Standard Model.
• To reconcile this $g-2$ excess with dark matter phenomenology, including relic abundance, direct and indirect detection constraints.
• To explore how increasing the number of internal degrees of freedom $n_f$ in the dark matter sector suppresses indirect detection signals and relaxes experimental bounds.
• To identify viable parameter space for a real scalar dark matter state and a charged fermionic mediator, both below 200 GeV, that satisfy all constraints.
• To identify future experimental probes, including high-luminosity LHC, lepton colliders, and gamma-ray telescopes like CTA and GAMMA-400.

Proposed method

• Introduce a lepton portal dark matter model with a real scalar dark matter particle $X$ and a charged fermionic mediator $\psi_\ell$, coupled via a $\lambda \overline{\psi}_\ell \psi_\ell X$ interaction term.
• Implement a global $S_{n_f}$ symmetry to treat the dark matter as a multiplet of $n_f$ degenerate states, reducing the required coupling $\lambda$ by $1/\sqrt{n_f}$ to fit $\Delta a_\mu$.
• Use one-loop calculations to compute the contribution to the muon anomalous magnetic moment, showing $\Delta a_\mu \propto \lambda^2 m_\mu^2 / \Lambda^2$ with $\Lambda \sim \text{mass splitting}$.
• Compute the thermal relic abundance via co-annihilation processes involving $X$ and $\psi_\ell$, using the Boltzmann equation and $s$-channel annihilation cross sections.
• Apply constraints from direct detection (spin-independent scattering), indirect detection (gamma-ray lines from three-body annihilation), and collider searches (soft leptons in compressed spectra).
• Assess perturbativity and Landau pole scales via one-loop beta function analysis, identifying UV completion limits.

Experimental results

Research questions

• RQ1 Can a lepton portal dark matter model with a real scalar dark matter and a charged fermionic mediator explain the observed $\Delta a_\mu$ excess while remaining consistent with dark matter relic abundance and direct detection?
• RQ2 How does increasing the number of internal degrees of freedom $n_f$ in the dark matter sector suppress indirect detection signals and relax constraints from gamma-ray line searches?
• RQ3 What are the viable mass ranges for the dark matter and charged mediator that satisfy $\Delta a_\mu$, relic density, and collider constraints?
• RQ4 At what energy scale does the model become non-perturbative, and how does this constrain the UV completion of the theory?
• RQ5 Which future experiments—high-luminosity LHC, lepton colliders, or gamma-ray telescopes—can most effectively test this model?

Key findings

• The model explains the observed $\Delta a_\mu = 251(59) \times 10^{-11}$ excess with a real scalar dark matter particle and a charged fermionic mediator, both with masses below approximately 200 GeV.
• With $n_f = 30$ internal degrees of freedom, the required coupling $\lambda$ to fit $\Delta a_\mu$ is reduced by a factor of $1/\sqrt{30} \approx 0.18$, suppressing indirect detection signals by a factor of $n_f^2 = 900$.
• Thermal dark matter co-annihilation can reproduce the observed relic abundance for $n_f \approx 45$ to $55$, with larger $n_f$ preferred to delay the Landau pole.
• The model remains perturbative up to scales of $\sim 2$ TeV, but the Landau pole appears at $\sim 500$ GeV to $2$ TeV depending on the coupling, indicating a limit on UV completion.
• Future high-luminosity LHC searches for soft leptons in compressed spectra and lepton colliders with $\sqrt{s} \gtrsim 500$ GeV can nearly fully probe the allowed parameter space.
• Indirect detection via gamma-ray lines from three-body annihilation is suppressed by $n_f^2$, making it consistent with Fermi-LAT constraints for $n_f \gtrsim 10$.