Dark Matter in the Singlet Extension of MSSM: Explanation of Pamela and Implication on Higgs Phenomenology

As discussed recently by Hooper and Tait, the singlino-like dark matter in the Minimal Supersymmetric Standard Model (MSSM) extended by a singlet Higgs superfield can give a perfect explanation for both the relic density and the Pamela result through the Sommerfeld-enhanced annihilation into singlet Higgs bosons ($a$ or $h$ followed by $h->a a$) with $a$ being light enough to decay dominantly to muons or electrons. In this work we analyze the parameter space required by such a dark matter explanation and also consider the constraints from the LEP experiments. We find that although the light singlet Higgs bosons have small mixings with the Higgs doublets in the allowed parameter space, their couplings with the SM-like Higgs boson $h_{SM}$ (the lightest doublet-dominant Higgs boson) can be enhanced by the soft parameter $A_\kappa$ and, in order to meet the stringent LEP constraints, the $h_{SM}$ tends to decay into the singlet Higgs pairs $aa$ or $hh$ instead of $b\bar b$. So the $h_{SM}$ produced at the LHC will give a multi-muon signal, h_{SM} -> aa -> 4 muons or h_{SM} -> hh -> 4 a -> 8 muons.