Natural Realization of Tens-of-GeV Dark Matter in the GNMSSM

TL;DR

The paper investigates the viability of light dark matter (DM) in supersymmetric frameworks by comparing MSSM, $Z_3$-NMSSM, and the General NMSSM (GNMSSM) under relic-density, LZ 2024, Higgs data, and LHC constraints. It shows that only the GNMSSM can naturally realize tens-of-GeV DM with a Singlino-like LSP, thanks to the decoupling of annihilation and direct-detection interactions via independent $\mu$ and $\mu'$ parameters, allowing $\lambda$ to be small while $\kappa$ can be larger. The study identifies two characteristic GNMSSM hierarchies, $\tilde{S}<\tilde{B}<\tilde{H}$ and $\tilde{S}<\tilde{H}<\tilde{B}$, and demonstrates that viable scenarios exist with DM masses in the 10–100 GeV range, where annihilation proceeds through secluded-sector channels and SI cross-sections are suppressed by destructive interference. LHC constraints depend crucially on the NLSP identity, with natural, low-$\mu_{\rm tot}$ solutions favored in the $\tilde{S}<\tilde{B}<\tilde{H}$ case, and significantly stronger bounds in the heavy-Bino scenario; overall the GNMSSM provides a coherent and less-tuned framework for achieving light DM compatible with current data, while offering distinctive collider and direct-detection signatures for future tests.

Abstract

This study presents a comparative analysis of the Minimal Supersymmetric Standard Model (MSSM), the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model ($Z_3$-NMSSM), and the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM), incorporating constraints from dark matter (DM) relic density, the LUX-ZEPLIN 2024 experiment (LZ 2024), Higgs data, and the Large Hadron Collider (LHC). The results suggest that, among the three frameworks, only GNMSSM can naturally accommodate for light DM with a mass below $100~{\rm GeV}$. As such, the viable supersymmetry candidate is primarily Singlino-like. One key advantage of the GNMSSM is the effective decoupling between interactions that establish the relic density and those that control direct detection, allowing the model to satisfy all current experimental bounds simultaneously. We further explore two characteristic mass hierarchies in the GNMSSM parameter space, each exhibiting distinct phenomenological behaviors. The first hierarchy, $\tilde{S} < \tilde{B} < \tilde{H}$ (Singlino--Bino--Higgsino), involves a relatively light Bino and allows the Higgsino mass parameter, $μ_{\rm tot}$, to be as low as about $200~{\rm GeV}$, naturally yielding light DM at tens of GeV. The dominant annihilation channels are then $\tildeχ_1^0\tildeχ_1^0 \to A_sA_s$ in the $h_1$ scenario and $\tildeχ_1^0\tildeχ_1^0 \to h_sA_s$ in the $h_2$ scenario, where $h_s$ and $A_s$ denote singlet-dominated CP-even and CP-odd Higgs bosons, respectively. The second hierarchy, $\tilde{S} < \tilde{H} < \tilde{B}$, corresponds to a heavy Bino. In this case, although the DM phenomenology remains qualitatively similar, LHC constraints require $μ_{\rm tot} \gtrsim 900~{\rm GeV}$, implying a significant degree of fine-tuning in reproducing the $Z$-boson mass.

Figures (5)

• Figure 1: Scatter plots for samples dominated by $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to A_s A_s$ annihilation and satisfying all experimental constraints in the $h_1$ scenario. Left panel: $|D| \equiv |(A_\kappa - m_{\tilde{S}})/m_{\tilde{\chi}_1^0}|$ versus $|m_{\tilde{\chi}_1^0}|$, with color scale $C_s$ defined by $2\{ \ln |(A_\kappa-m_{\tilde{S}})/m_{\tilde{\chi}^0_1} | -\ln |(m_{h_s}/m_{\tilde{\chi}^0_1})^2-4)| \}$, indicating relative $s$-channel strength in Eq. (\ref{['eq:sigvAsAs2']}). Right panel: $|\kappa|$ versus $|m_{\tilde{\chi}_1^0}|$, colored by the squared mass ratio $R_1 \equiv (m_{A_s}/m_{\tilde{\chi}_1^0})^2$.
• Figure 2: Scatter plots for samples dominated by $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to h_s A_s$ annihilation and satisfying all experimental constraints in the $h_2$ scenario. Left panel: $R_2 \equiv (m_{h_s}/m_{\tilde{\chi}_1^0})^2$ versus $|m_{\tilde{\chi}_1^0}|$, with a color bar $C_t$ defined by $8 m_{A_s}^2/(4 m_{\tilde{\chi}^0_1}^2- m_{h_s}^2)$, which measures the partial $t$-channel contributions of Eq. (\ref{['eq:sigvPhiPhi1']}). Right panel: $|\kappa|$ versus $|m_{\tilde{\chi}_1^0}|$, with a color bar representing the $s$-channel contribution $D\equiv (A_\kappa - m_{\tilde{S}})/m_{\tilde{\chi}_1^0}$ in Eq. (\ref{['eq:sigvPhiPhi1']}).
• Figure 3: Scatter plots of $\sigma_{\rm eff}^{\rm SI}$ versus $|m_{\tilde{\chi}^0_1}|$ for the samples in the $h_1$ scenario (left panel) and the $h_2$ scenario (right panel). The color bar is defined as $\ln (\lambda |\kappa|)$, describing the coupling strength involved in the scattering.
• Figure 4: LHC constraints on the parameters $|m_{\tilde{\chi}_1^0}|$, $\mu_{\rm tot}$, $|\kappa|$, and $\lambda$. Samples include those obtained by the scans and refined by the LZ 2024 constraints. They are classified by exclusion levels, as depicted in the legend. Gray markers are excluded by SModelS-3.0.0, blue markers ($R < 1$) are consistent with all experiments, and red markers ($R \ge 1$) are excluded by LHC data. The upper panels correspond to the $h_1$ scenario, while the lower panels refer to the $h_2$ scenario.
• Figure 5: Similar to Fig. \ref{['fig:LHC-h1h2-150']}, but for $M_1=2~\rm{TeV}$ in the $h_1$ scenario. Samples with $R \geq 1$ are further categorized: green markers ($1 \leq R \leq 1.5$) represent those satisfying the loose LHC constraint criterion, suggesting potential compatibility with LHC data once theoretical and experimental uncertainties are properly accounted for. These uncertainties arise from multiple sources, including sparticle production cross-section calculations and involved Monte Carlo simulations.