Singlino-dominated dark matter in general NMSSM

The general Next-to-Minimal Supersymmetric Standard Model (NMSSM) describes the singlino-dominated dark-matter (DM) property by four independent parameters: singlet-doublet Higgs coupling coefficient $\lambda$, Higgsino mass $\mu_{tot}$, DM mass $m_{\tilde{\chi}_1^0}$, and singlet Higgs self-coupling coefficient $\kappa$. The first three parameters strongly influence the DM-nucleon scattering rate, while $\kappa$ usually affects the scattering only slightly. This characteristic implies that singlet-dominated particles may form a secluded DM sector. Under such a theoretical structure, the DM achieves the correct abundance by annihilating into a pair of singlet-dominated Higgs bosons by adjusting $\kappa$'s value. Its scattering with nucleons is suppressed when $\lambda v/\mu_{tot}$ is small. This speculation is verified by sophisticated scanning of the theory's parameter space with various experiment constraints considered. In addition, the Bayesian evidence of the general NMSSM and that of $Z_3$-NMSSM is computed. It is found that, at the cost of introducing one additional parameter, the former is approximately $3.3 \times 10^3$ times the latter. This result corresponds to Jeffrey's scale of 8.05 and implies that the considered experiments strongly prefer the general NMSSM to the $Z_3$-NMSSM.