Singlino-dominated dark matter in $Z_3$-NMSSM.

Singlino-dominated dark matter properties are investigated in the $Z_3$-NMSSM, producing superweak interactions with nucleons involved in dark matter direct detection experiments. Approximate analytic formulas describing the dark matter abundance and cross-section in scattering with nucleons are used to illustrate a dependence on theory parameters in neutralino and Higgs sectors. It is shown that the measured abundance requires a sizable singlet-doublet Higgs coupling parameter $\lambda$, while the detection experimental results prefer a small $\lambda$. The parameter space is then surveyed using a nest sampling technique guided by a likelihood function containing various observables in dark matter, Higgs, and B physics, such as the abundance and the scattering cross-section. It is demonstrated that dark matter can achieve the correct abundance through $\tilde{\chi}_1^0 \tilde{\chi}_1^0 \to t \bar{t}$ or a co-annihilation with higgsinos. The former process provides a significantly larger Bayesian evidence than the latter, but it will be entirely excluded by the near future PandaX-4T experiment. Three mechanisms are summarized to suppress dark matter scattering with nucleons, namely a small $\lambda$ and two kinds of cancellation between different contributions.