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

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, $\mu_{\rm tot}$, to be as low as about $200~{\rm GeV}$, naturally yielding light DM at tens of GeV. The dominant annihilation channels are then $\tilde{\chi}1^0\tilde{\chi}_1^0 \to A_sA_s$ in the $h_1$ scenario and $\tilde{\chi}_1^0\tilde{\chi}_1^0 \to h_sA_s$ 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 $\mu{\rm tot} \gtrsim 900~{\rm GeV}$, implying a significant degree of fine-tuning in reproducing the $Z$-boson mass.