Dark Matter Physics in General NMSSM

In the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM), singlet particles may form a secluded sector of dark matter (DM), in which Singlino-like DM could achieve the observed relic abundance through various channels such as $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to h_s h_s, A_s A_s, h_s A_s$, where $h_s$ and $A_s$ represent singlet-dominated CP-even and CP-odd Higgs bosons. We provide analytical formulas for both the spin-independent and spin-dependent cross sections of Singlino DM scattering with nucleons, illustrating their dependence on the model's parameters in a clear manner. We also present analytic expressions for the annihilation cross sections of these three important channels. Based on these preparations, we conducted Bayesian analyses of the GNMSSM and concluded that the theory significantly favored Singlino-dominated DM over Bino-like DM across a much broader range of parameters. The combined results from our numerical analyses and the formulas distinctly highlight crucial aspects of DM physics within the GNMSSM.