  Due to the limited statistics so far accumulated in the Higgs boson search at
the LHC, the Higgs boson property has not yet been tightly constrained and it
is still allowed for the Higgs boson to decay invisibly to dark matter with a
sizable branching ratio. In this work, we examine the Higgs decay to neutralino
dark matter in low energy SUSY by considering three different models: the
minimal supersymmetric standard model (MSSM), the next-to-minimal
supersymmetric standard models (NMSSM) and the nearly minimal supersymmetric
standard model (nMSSM). Under current experimental constraints at 2-sigma level
(including the muon g-2 and the dark matter relic density), we scan over the
parameter space of each model. Then in the allowed parameter space we calculate
the branching ratio of the SM-like Higgs decay to neutralino dark matter and
examine its observability at the LHC by considering three production channels:
the weak boson fusion VV->h, the associated production with a Z-boson pp->hZ+X
or a pair of top quarks pp->htt_bar+X. We find that in the MSSM such a decay is
far below the detectable level; while in both the NMSSM and nMSSM the decay
branching ratio can be large enough to be observable at the LHC.
