In the natural realization of the Next-to-minimal Supersymmetric Standard Model, Higgsinos tend to be lighter than about several hundred GeVs, which can induce detectable leptonic signals at the LHC as well as large DM-nucleon scattering cross section. We explore the constraints from the direct searches for electroweakino and slepton at the LHC Run II and the latest DM direct detection experiments on the scenario with low fine tuning indicator ∆ Z/h ≤ 50. We find that these experiments are complementary to each other in excluding the scenario, and as far as each kind of experiment is concerned, it is strong enough to exclude a large portion of the parameter space. As a result, the scenario with Bino-or Higgsinodominated DM is disfavored, and that with Singlino-dominated DM is tightly limited. There are two regions in natural NMSSM parameter space surviving in the current experimental limits. One is featured with a decoupled Singlino-dominated LSP with µ m χ 0 1 , which cannot be explored by neither DM detections or collider searches. The other parameter space region is featured by 10 −47 cm 2 σ SI χ−p 10 −46 cm 2 and the correlation µ m χ 0 1 , which will be explored by near future DM detection experiments.

So far dark matter direct detection experiments have indicated any dark matter particle to have feeble interactions with nucleons, while the dark relic matter density favors it to take part in weak interactions. We point out that the neutralino dark matter in the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM) fails to process these two seemingly contradictory features in their most natural parameter space due to the limited theoretical structure. By contrast, the seesaw extension of the NMSSM, which was originally proposed to solve neutrino mass problem, enables the lightest sneutrino as a new viable DM candidate to readily have the features, and thus satisfies the constraints of the DM measurements in its broad parameter space. Compared with the Type-I seesaw extension, the dark matter physics in the inverse seesaw extension is more flexible to be consistent with current dark matter and collider experimental results. We conclude that the weakly interacting massive particles in supersymmetric theory is still a promising dark matter candidate.

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 Next-to Minimal Supersymmetric Standard Model (NMSSM) with a Type-I seesaw mechanism extends the NMSSM by three generations of right-handed neutrino fields to generate neutrino mass. As a byproduct it renders the lightest sneutrino as a viable DM candidate. Due to the gauge singlet nature of the DM, its scattering with nucleon is suppressed in most cases to coincide spontaneously with the latest XENON-1T results. Consequently, broad parameter spaces in the Higgs sector, especially a light Higgsino mass, are resurrected as experimentally allowed, which makes the theory well suited to explain the long standing bb excess at LEP-II and the continuously observed γγ excess by CMS collaboration. We show by both analytic formulas and numerical results that the theory can naturally predict the central values of the excesses in its broad parameter space, and the explanations are consistent with the Higgs data of the discovered Higgs boson, B−physics and DM physics measurements, the electroweak precision data as well as the LHC search for sparticles. Part of the explanations may be tested by future DM experiments and the SUSY search at the LHC.

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