Dark matter in the NMSSM with small $\lambda$ and $\kappa$

The NMSSM provides an excellent dark matter candidate, usually, the lightest neutralino ($\tilde{\chi}^0_1$) being the lightest supersymmetric particle (LSP), in the universe. It is a mixture of the bino, the neutral wino, the neutral higgsinos, and the singlino. In this work, we investigate the features of the lightest neutralino by concentrating on a specific region of the NMSSM parameter space with small values of both $\lambda$ and $\kappa$, taking into account theoretical and experimental constraints, including relic density, direct and indirect detection constraints. We have found that the LSP dark matter is a singlino-dominated neutralino for most of the sample points of the chosen scenario. Thus, contrary to expectations, the NMSSM is not comparable to the MSSM in terms of dark matter properties as $\lambda$ and $\kappa$ are very small. The LSP can also be either higgsino-dominated or bino-dominated in some parameter space. The most important parameters affecting the mass and properties of the LSP are $\kappa$, $\lambda/\kappa$, and $\mu_{\rm eff}$. Further, we notice that $\sigma^{SI}_p \approx 1.02$ $\sigma^{SI}_n$ and $\sigma^{SD}_p \approx 0.76$ $\sigma^{SD}_n$ for all the surviving sample points.