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In this note we briefly review the recent studies of dark matter in the MSSM and its singlet extensions: the NMSSM, the nMSSM, and the general singlet extension. Under the new detection results of CDMS II, XENON, CoGeNT, and PAMELA, we find that (i) the latest detection results can exclude a large part of the parameter space which is allowed by current collider constraints in these models. The future SuperCDMS and XENON can cover most of the allowed parameter space; (ii) the singlet sector will decouple from the MSSM-like sector in the NMSSM; however, singlet sector makes the nMSSM quite different from the MSSM; (iii) the NMSSM can allow light dark matter at several GeV to exist. Light CP-even or CP-odd Higgs boson must be present so as to satisfy the measured dark matter relic density. In case of the presence of a light CP-even Higgs boson, the light neutralino dark matter can explain the CoGeNT and DAMA/LIBRA results; (iv) the general singlet extension of the MSSM gives a perfect explanation for both the relic density and the PAMELA result through the Sommerfeld-enhanced annihilation. Higgs decays in different scenario are also studied.

Although there are many theoretical or aesthetical arguments for the necessity of TeV-scale new physics, the most convincing evidence is from the (Wilkinson Microwave Anisotropy Probe) WMAP observation of the cosmic cold dark matter, which naturally indicates the existence of (weakly interacting massive particles) WIMPs beyond the prediction of the standard model (SM). By contrast, the neutrino oscillations may rather imply trivial new physics (plainly adding right-handed neutrinos to the SM) or new physics at some very high see-saw scale unaccessible to any foreseeable colliders. Therefore, the TeV-scale new physics to be unraveled at the large hadron collider (LHC) is the most likely related to the WIMP dark matter.

If WIMP dark matter is chosen by nature, it will give a strong argument for low-energy supersymmetry (SUSY) with R parity which can give a good candidate. Nevertheless, SUSY is motivated for solving the hierarchy problem elegantly. It can also solve other puzzles of the SM, such as the

If we introduce a singlet superfield to the MSSM, the Higgs sector will have one more CP even component and one more CP odd component, and the neutralino sector will have one more singlino component. These singlet multiplets compose a “singlet sector” of the MSSM. It can make the phenomenologies of SUSY dark matter and Higgs different from the MSSM. More and more precision results of dark matter detection give us an opportunity to test if this singlet sector really exists. For example, experiments for the underground direct detection of cold dark matter

In this paper, we will give a short review on the difference between the MSSM and the MSSM with a singlet sector under the constraints of new dark matter detection results. As the Higgs hunting on colliders has delicate relation with dark matter detections, the implication on Higgs searching is also reviewed. The content is based on our previous work [

As an economical realization of supersymmetry, the MSSM has the minimal content of particles, while the NMSSM and the nMSSM extend the MSSM by only adding one singlet Higgs superfield

Corresponding to the superpotential, the Higgs soft terms in the scalar potentials are also different between the three models (the soft terms for gauginos and sfermions are the same thus not listed here)

The MSSM predicts four neutralinos

For a moderate value of

Since the

The chargino sector of these three models is the same except that in the NMSSM/nMSSM the parameter

First let us see the MSSM, the NMSSM, and the nMSSM under the constraints of results of CDMS II and XENON100. As both current and future limits of

For the calculation of cross-section of

Considering all the constraints listed above, we scan over the parameters in the following ranges:

The surviving points for the three model are displayed in Figure

The scatter plots (taken for [

From Figure

Same as Figure

Same as Figure

In Figure

Same as Figure

From the survived parameter space for all the model above, we should know that the Higgs decay will be similar for the MSSM and the NMSSM, but quite different from the nMSSM. This can be seen in Figure

Same as Figure

As we talked in the introduction, the data of CoGeNT experiment favors a light dark matter around 10 GeV. However, we scan the parameter space in the MSSM and find that it is very difficult to find a neutralino

Now we discuss how to get a light

In Figure

The scatter plots (taken for [

In the light

Same as Figure

Since the conventional decay modes of

Same as Figure

Figure

To explain the PAMELA excess by dark matter annihilation, there are some challenges. First, dark matter must annihilate dominantly into leptons since PAMELA has observed no excess of antiprotons [

The above fancy idea is hard to realize in the MSSM, because there is not a new force in the neutralino dark matter sector to induce the Sommerfeld enhancement, and neutralino dark matter annihilates largely to final states consisting of heavy quarks or gauge and/or Higgs bosons [

The singlino dark matter annihilates to the light singlet Higgs bosons, and the relic density can be naturally obtained from the interaction between singlino and singlet Higgs bosons.

The singlet Higgs bosons, not related to electroweak symmetry breaking, can be light enough to be kinematically allowed to decay dominantly into muons or electrons through the tiny mixing with the Higgs doublets.

The Sommerfeld enhancement needed in dark matter annihilation for the explanation of PAMELA result can be induced by the light singlet Higgs boson.

If we introduce a singlet Higgs to the MSSM in general, the renormalizable holomorphic superpotential of Higgs is given by [

The CP-even Higgs mass matrix in the basis

The CP-odd Higgs mass matrix

The charged Higgs mass matrix

The neutralino mass matrix is

To explain the observation of PAMELA,

Feynman diagrams for singlino dark matter annihilation where Sommerfeld enhancement is induced by exchanging

The numerical results of this model are displayed in different planes in Figures

The scatter plots showing the decay branching ratios

Same as Figure

Same as Figure

In left plot of Figure

Finally, we note that, for the specified singlet extensions like the nMSSM and the NMSSM, the explanation of PAMELA and relic density through Sommerfeld enhancement is not possible. The reason is that the parameter space of such models is stringently constrained by various experiments and dark matter relic density as shown in the above section, and, as a result, the neutralino dark matter may explain either the relic density or PAMELA, but impossible to explain both via Sommerfeld enhancement. For example, in the nMSSM various experiments and dark matter relic density constrain the neutralino dark matter particle in a narrow mass range [

At last we summarize here the SUSY dark matter, and Higgs physics will be changed if we introduce a singlet to the MSSM. Under the latest results of dark matter detection, we have the following.

In the MSSM, the NMSSM, and the nMSSM, the latest detection result can exclude a large part of the parameter space allowed by current collider constraints, and the future SuperCDMS and XENON can cover most of the allowed parameter space.

Under the new dark matter constraints, the singlet sector will decouple from the MSSM-like sector in the NMSSM; thus, the phenomenologies of dark matter and Higgs are similar to the MSSM. The singlet sector makes the nMSSM quite different from the MSSM, the LSP in the nMSSM is singlet dominant, and the SM-like Higgs will mainly decay into the singlet sector. Future precision measurements will give us an opportunity to determine whether the new scalar is from standard model or from SUSY. Perhaps the nMSSM will be the first model excluded for its much larger branching ratio of invisible Higgs decay.

The NMSSM can allow light dark matter at several GeV to exist. Light CP-even or CP-odd Higgs boson must be present so as to satisfy the measured dark matter relic density. In case of the presence of a light CP-even Higgs boson, the light neutralino dark matter can explain the CoGeNT and DAMA/LIBRA results. Further, we find that in such a scenario the SM-like Higgs boson will decay predominantly into a pair of light Higgs bosons or a pair of neutralinos, and the conventional decay modes will be greatly suppressed.

The general singlet extension of the MSSM gives a perfect explanation for both the relic density, and the PAMELA result through the Sommerfeld enhanced annihilation into singlet Higgs bosons (

This work was supported in part by the NSFC no. 11005006, no. 11172008, and Doctor Foundation of BJUT no. X0006015201102.