Theoretical and Experimental Constraints on $\mathbb{Z}_{2n}$ Multi-Component Dark Matter Models

TL;DR

By confronting three Z2n-stabilized two-component scalar DM models with Planck relic abundance and LZ direct-detection data, and by imposing one-loop RGE–driven vacuum stability and perturbative unitarity up to the GUT/Planck scales, the paper maps the viable parameter spaces and reveals distinct high-energy implications for each model. The Z4 scenario emerges as broadly viable thanks to efficient semi-annihilation; the Z6(23) model is consistent only as a low-energy effective theory requiring UV completion below ~$10^6$ GeV, signaling new PeV-scale physics; the Z6(13) model remains highly fine-tuned, with viable points confined near the Higgs resonance. The results demonstrate the power of combining DM phenomenology with high-scale theoretical consistency to constrain beyond-the-Standard-Model scenarios and hint at concrete directions for UV completions and future experimental tests, including gravitational-wave probes of the electroweak sector and potential SUSY extensions. The study provides a practical framework for evaluating multi-component DM models by jointly accounting for thermal history, direct detection, and high-energy consistency checks.

Abstract

A complete assessment of any dark matter model requires confronting its low-energy phenomenology with its high-scale theoretical viability. We undertake such a dual analysis for a class of two-component scalar dark matter models stabilized by $\mathbb{Z}_{2n}$ symmetries, specifically the $\mathbb{Z}_4$, $\mathbb{Z}_6(23)$, and $\mathbb{Z}_6(13)$ frameworks. Each model is tested against the latest observational data, including the Planck relic abundance and stringent direct detection limits from the LUX-ZEPLIN (LZ) experiment. Simultaneously, we evaluate their theoretical integrity up to the GUT and Planck scales by enforcing vacuum stability and perturbative unitarity with one-loop Renormalization Group Equations. This combined approach reveals a rich and varied landscape of possibilities. We demonstrate that the $\mathbb{Z}_4$ model offers a broadly viable parameter space sustained by efficient semi-annihilation. In stark contrast, the $\mathbb{Z}_6(13)$ scenario is shown to be highly fine-tuned, with solutions confined to the Higgs resonance. Our most significant finding concerns the $\mathbb{Z}_6(23)$ model: we show that an apparent conflict between experimental data and high-scale consistency is resolved when the model is viewed as an effective field theory, yielding a concrete prediction for new physics at or below the $10^6$ GeV scale. This work provides a definitive guide to the viability of these $\mathbb{Z}_{2n}$ scenarios and serves as a compelling demonstration of how high-energy consistency checks can yield crucial insights into the nature of dark matter.

Figures (15)

• Figure 1: Comparison of tree-level and RG-improved perturbative unitarity bounds in the $(\lambda_{HA}, \lambda_{HB})$ plane for the $\mathbb{Z}_4$ model (Scenario 1). The plots highlight the powerful impact of the quantum analysis on the unitarity constraints: while the tree-level calculation allows for couplings in a wide range, roughly $|\lambda_{Hi}| \lesssim 8\pi$, requiring unitarity to hold up to high energies under RG evolution restricts the viable parameter space to the much smaller region where $|\lambda_{Hi}| \lesssim 1$. The initial conditions for the fixed couplings are $\lambda_H \simeq 1/8$, $\lambda_A = 0.03$, $\lambda_B = 0.02$, $\lambda_{AB} = 0.25$, and $\lambda_{S4} = 0.01$. Similar results hold for the other models.
• Figure 2: A map of the parameter dependencies for the $\mathbb{Z}_{2n}$ models, which guides our numerical analysis strategy. The colored columns indicate whether a parameter (rows) influences the relic density (blue), direct detection (green), or the theoretical constraints (orange), with a filled circle ($\bullet$) marking a dependency. The final three columns use a checkmark ($\checkmark$) to show which parameters are present in each specific model. Note that some parameters are unique to a single model: $\mu_{S1}$ and $\lambda_{S4}$ ($\mathbb{Z}_4$); $\mu_{S2}$ ($\mathbb{Z}_6(23)$); and $\lambda'_{AB}$ ($\mathbb{Z}_6(13)$).
• Figure 3: Theoretically consistent regions in the $(\lambda_{HA}, \lambda_{HB})$ plane for the two benchmark scenarios of the $\mathbb{Z}_4$ model (see Table \ref{['tab:UnifiedScenariosValues']}). The color coding denotes regions that are: stable up to the Planck scale (dark green); stable only up to the GUT scale (light green); unstable at a high scale (red); or non-perturbative (orange). The dashed and dot-dashed lines indicate the boundaries of classical stability and perturbative unitarity, respectively.
• Figure 4: Phenomenology of the viable parameter space for the $\mathbb{Z}_4$ model. The three panels collectively illustrate how the semi-annihilation process, governed by the trilinear coupling $\mu_{S1}$, shapes the model's characteristics. This dynamic leads to the lighter component, $S_A$, dominating the relic density and ensures a non-degenerate mass spectrum, as detailed in the subcaptions.
• Figure 5: Direct detection prospects for the $\mathbb{Z}_4$ model, showing the rescaled spin-independent cross-section versus mass for each DM component ($S_A$, top; $S_B$, bottom) in Scenario 1 (left) and Scenario 2 (right). The plots highlight the powerful constraining impact of the latest LZ (2024) data (dashed black line) compared to the previous LZ (2023) limit (solid blue line). Points are colored by their status: excluded by LZ (2024) (black and gray), or, if viable, by their high-scale theoretical stability (red, light/dark green). A significant population of viable points remains above the neutrino floor (dashed orange line), indicating strong prospects for future discovery.