\begin{document}$\tilde{\chi}^0_1$\end{document} in the NMSSM-NUHM, and hence, it is small for highly singlino-dominated dark matter. (ii) The higgsino-mass parameter \begin{document}$\mu_{\rm{eff}}$\end{document} is smaller than approximately \begin{document}$335\;{\rm{GeV}}$\end{document} in the NMSSM-NUHM due to the current muon g-2 constraint, but our scenario with light dark matter can still be alive under current constraints including the direct detection of dark matter in the spin-dependent channel. (iii) With a sizeable higgsino component in the light dark matter, the higgsino asymmetry and SD cross section can also be sizeable, but dark matter relic density is always small; thus, it can escape the direct detections. (iv) Light dark matter in the \begin{document}$h_2$\end{document}- and Z-funnel annihilation channels with sufficient relic density can be covered by future LUX-ZEPLIN (LZ) 7-ton in SD detections. (v) The spin-independent (SI) cross section is dominated by \begin{document}$h_1$\end{document}- and \begin{document}$h_2$\end{document}-exchanging channels, which can even cancel each other in some samples, leaving an SI cross section smaller by a few orders of magnitude than that of one individual channel."> Higgsino asymmetry and direct-detection constraints of light dark matter in the NMSSM with non-universal Higgs masses -
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