WIMP Dark Matter from a Natural Discrete Gauge Symmetry in the Standard Model

TL;DR

The paper identifies a theoretically motivated WIMP dark matter candidate $χ_1$ arising from anomaly-free discrete gauge symmetries $\mathbb Z_4 \times \mathbb Z_3$ embedded in the SM. Anomaly cancellation with three right-handed neutrinos and three Majorana fermions $χ_i$ yields a stable $χ_1$ after symmetry breaking, with its mass set by a weak-scale singlet vev $v_\varphi$ and a scalar mediator $φ$ that mixes with the Higgs, enabling thermal freeze-out via a secluded Higgs-portal. The authors map viable relic-density regions in the $(m_{χ_1},m_s)$ plane across different $v_\varphi$, $\kappa$, and $s_\theta$, highlighting regimes with forbidden channels, resonant enhancement, and coannihilation; they show that destructive interference between the $h$ and $s$ mediators can suppress direct-detection signals, allowing compatibility with current bounds while remaining testable in future Xenon experiments and possibly offering collider hints around a light scalar near $m_s\sim 95$ GeV. This framework provides a non-SUSY realization of the WIMP paradigm tightly connected to SM structure, with clear experimental handles in both direct detection and collider searches.

Abstract

The internal structure of the Standard Model implies a natural $\mathbb{Z}_4 \times \mathbb{Z}_3$ discrete gauge symmetry. Cancellation of the corresponding Dai--Freed anomalies requires the introduction of three right-handed neutrinos and three additional Majorana fermions $χ_i$. This gauge symmetry forbids the decay of the lightest fermion $χ_1$ into Standard Model particles, rendering it automatically stable and providing a dark matter candidate without introducing an ad hoc stabilizing symmetry and domain-wall problem. The mass of $χ_1$ is generated by the vacuum expectation value of a singlet scalar near the electroweak scale, naturally realizing a weakly interacting massive particle (WIMP) freeze-out scenario. Dark matter annihilation proceeds through scalar mediation, allowing the observed relic abundance to be reproduced while remaining consistent with current direct-detection constraints. It naturally realizes the secluded dark matter scenario and can be further tested in the next generation of experiments.

Figures (4)

• Figure 1: Number changing diagrams involving $\chi_1$ that are relevant to DM genesis, where $X$ denotes the possible SM fermion and vector boson final states.
• Figure 2: Number changing diagrams involving coannihilating $\chi_1$ and $\chi_i$. The cross denotes the effective intra-generation mixing among $\chi_i\chi_1$ induced by $\Phi$.
• Figure 3: Relic density of dark matter particle $\chi_1$ as a function of its mass $m_{\chi_1}$ and the scalar mass $m_s$. Different colored regions correspond to different relic density values. Each subfigure corresponds to different values of the parameters $v_\varphi, \kappa, \theta$.
• Figure 4: Comparison between the DM–nucleon scattering cross section predicted in our model and current direct-detection limits. The gray and blue shaded regions indicate the neutrino fog and the exclusions from direct-detection experiments, respectively. The red (purple) solid (dashed) curve shows the scattering cross section that reproduces the observed relic abundance $\Omega h^2 = 0.12$ for fixed ratio of $m_s = 0.5 (0.35) m_{\chi_1}$ and $\sin \theta = 0.001 (0.05)$. The dark-red solid curve represents the case $m_s > m_\chi$ with $\kappa = -12\,$TeV, $v_\varphi = 1\,$TeV, and $\sin \theta = 0.1$.