Dark matter in the MSSM and its singlet extension

We briefly review the supersymetric explanation for the cosmic dark matter. Although the neutralino in the minimal supersymmetric model (MSSM), the next-to-minimal supersymmetric model (NMSSM) and the nearly minimal supersymmetric model (nMSSM) can naturaly explain the dark matter relic density, the PAMELA result can hardly be explained in these popular models. In the general singlet extension of the MSSM, both the PAMELA result and the relic density can be explained by the singlino-like neutralino. Such singlino-like neutralinos annihilate into the singlet-like Higgs bosons, which are light enough to decay dominantly to muons or electrons, and the annihilation cross section can be greatly enhanced by the Sommerfeld effect via exchanging a light CP-even singlet-like Higgs boson. In this scenario, in order to meet the stringent LEP constraints, the SM-like Higgs boson tends to decay into the singlet Higgs pairs instead of $b\bar b$ and consequently it will give a multi-muon signal $h_SM->aa->\mu$ or $h_{SM}->hh->4 a ->8 \mu$ at the LHC.