In the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with extra heavy neutrino superfields, neutrino may acquire its mass via a seesaw mechanism and sneutrino may act as a viable dark matter (DM) candidate. Given the strong tension between the naturalness for Z boson mass and the DM direct detection experiments for customary neutralino DM candidate, we augment the NMSSM with Type-I seesaw mechanism, which is the simplest extension of the theory to predict neutrino mass, and study the scenarios of sneutrino DM. We construct likelihood function with LHC Higgs data, B-physics measurements, DM relic density and its direct and indirect search limits, and perform a comprehensive scan over the parameter space of the theory by Nested Sampling method. We adopt both Bayesian and frequentist statistical quantities to illustrate the favored parameter space of the scenarios, the DM annihilation mechanism as well as the features of DMnucleon scattering. We find that the scenarios are viable over broad parameter regions, especially the Higgsino mass µ can be below about 250GeV for a significant part of the region, which predicts Z boson mass in a natural way. We also find that the DM usually co-annihilated with the Higgsinos to get the measured relic density, and consequently the DM-nucleon scattering rate is naturally suppressed to coincide with the recent XENON-1T results even for light Higgsinos. Other issues, such as the LHC search for the Higgsinos, are also addressed.1 Numerically speaking, the mixing angle should satisfy sin θν ∼ 0.02 for mν = 100GeV to predict the right DM relic density by the Z boson mediated annihilation, which corresponds to the scattering rate at the order of 10 −45 cm −2 [34]. Such a rate has been excluded by the latest XENON-1T experiment, which, on the other side, limits sin θν < 0.01 by the recent calculation in [35]. Moreover, we find that the correlation between the relic density and the scattering rate is underestimated in FIG.1 of [36].

In supersymmetric theories like the Next-to-Minimal Supersymmetric Standard Model (NMSSM), the lightest neutralino with bino or singlino as its dominant component is customarily taken as dark matter (DM) candidate. Since light Higgsinos favored by naturalness can strength the couplings of the DM and thus enhance the DM-nucleon scattering rate, the tension between naturalness and DM direct detection results becomes more and more acute with the improved experimental sensitivity. In this work, we extend the NMSSM by inverse seesaw mechanism to generate neutrino mass, and show that in certain parameter space the lightest sneutrino may act as a viable DM candidate, i.e. it can annihilate by multi-channels to get correct relic density and meanwhile satisfy all experimental constraints. The most striking feature of the extension is that the DM-nucleon scattering rate can be naturally below its current experimental bounds regardless of the higgsino mass, and hence it alleviates the tension between naturalness and DM experiments. Other interesting features include that the Higgs phenomenology becomes much richer than that of the original NMSSM due to the relaxed constraints from DM physics and also due to the presence of extra neutrinos, and that the signatures of sparticles at colliders are quite different from those with neutralino as DM candidate.

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.

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.

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.