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Very recently, a Fermilab report of muon $g-2$ showed a $4.2\sigma$discrepancy between it and the standard model (SM) prediction. Motivated bythis inspiring result and the increasing tension in supersymmetricinterpretation of the anomalous magnetic moment, it is argued that in thegeneral next-to-minimal supersymmetric standard model (GNMSSM), asinglino-dominated neutralino can act as a feasible dark matter (DM) candidatein explaining the discrepancy naturally. In this case, the singlino-dominatedDM and singlet-dominated Higgs bosons can form a secluded DM sector with$\tilde{\chi}_1^0\tilde{\chi}_1^0 \to h_s A_s$ responsible for the measured DMrelic abundance. when $m_{\tilde{\chi}_1^0} \gtrsim 150~{\rm GeV}$ and theYukawa coupling $\kappa$ is around $0.2$. This sector communicates with the SMsector by weak singlet-doublet Higgs mixing, so the scatterings of thesinglino-dominated DM with nucleons are suppressed. Furthermore, due to thesinglet nature of the DM and the complex mass hierarchy, sparticle decay chainsin the GNMSSM are lengthened in comparison with the prediction of the minimalsupersymmetric standard model. These characteristics lead to sparticledetection at the Large Hadron Collider (LHC) being rather tricky. This studysurveys a specific scenario of the GNMSSM, which extends the$\mathbb{Z}_3$-NMSSM by adding an explicit $\mu$-term, to reveal the features.It indicates that the theory can readily explain the discrepancy of the muonanomalous magnetic moment without conflicting with the experimental results inDM and Higgs physics, and the LHC searches for sparticles.

Improved $(g-2)_\mu$ measurement and singlino dark matter in $\mu$-term extended $\mathbb{Z}_3$-NMSSM