Very recently, a Fermilab report of muon g− 2 showed a 4.2σ discrepancy between it and the standard model (SM) prediction. Motivated by this inspiring result and the increasing tension in supersymmetric interpretation of the anomalous magnetic moment, it is argued that in the general next-to-minimal supersymmetric standard model (GNMSSM), a singlino-dominated neutralino can act as a feasible dark matter (DM) candidate in explaining the discrepancy naturally. In this case, the singlino-dominated DM and singlet-dominated Higgs bosons can form a secluded DM sector with $$ {\overset{\sim }{\chi}}_1^0{\overset{\sim }{\chi}}_1^0 $$ χ ~ 1 0 χ ~ 1 0 → hsAs responsible for the measured DM relic abundance when $$ {m}_{{\overset{\sim }{\chi}}_1^0} $$ m χ ~ 1 0 ≳ 150 GeV and the Yukawa coupling κ is around 0.2. This sector communicates with the SM sector by weak singlet-doublet Higgs mixing, so the scatterings of the singlino-dominated DM with nucleons are suppressed. Furthermore, due to the singlet nature of the DM and the complex mass hierarchy, sparticle decay chains in the GNMSSM are lengthened in comparison with the prediction of the minimal supersymmetric standard model. These characteristics lead to sparticle detection at the Large Hadron Collider (LHC) being rather tricky. This study surveys a specific scenario of the GNMSSM, which extends the ℤ3-NMSSM by adding an explicit μ-term, to reveal the features. It indicates that the theory can readily explain the discrepancy of the muon anomalous magnetic moment without conflicting with the experimental results in DM and Higgs physics, and the LHC searches for sparticles.

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 λ, Higgsino mass μtot, DM mass $$ {m}_{{\tilde{\chi}}_1^0} $$ m χ ˜ 1 0 , and singlet Higgs self-coupling coefficient κ. The first three parameters strongly influence the DM-nucleon scattering rate, while κ 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 κ’s value. Its scattering with nucleons is suppressed when λv/μtot 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 Z3-NMSSM is computed. It is found that, at the cost of introducing one additional parameter, the former is approximately 3.3 × 103 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 Z3-NMSSM.

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The present work investigates the possibility that both dark matter and the anomalous magnetic moment of the muon may be explained within the context of the inverse seesaw extended next-to-minimal supersymmetric Standard Model (ISS-NMSSM). In ISS-NMSSM, the newly introduced Higgs-neutrino Yukawa coupling Y ν provides additional Higgsino-sneutrino loop contribution to ðg − 2Þ μ. If the deviation between the experimental observations and the Standard Model predictions of the anomalous muon magnetic moment is confirmed by the further experimental and theoretical studies, it can be explained naturally within the ISS-NMSSM framework without conflicting with the current stringent limits on the direct detection of dark matter and Large Hadron Collider searches.