  If the Higgs boson were the only particle within the LHC accessible range,
precision measurement of the Higgs's properties would play a unique role in
studying electroweak symmetry breaking as well as possible new physics. We try
to use low energy experiments such as rare B decay to constrain a challenging
decay mode of Higgs, in which a Higgs decays to a pair of light (\approx 1 \sim
2 GeV) SM singlet S and becomes invisible. By using the current experimental
bound of rare decay B\to K\nu\bar{\nu} and computing the contribution of B\to K
SS to (the) B\to K+\cancel{E}, we obtain an upper bound on the Higgs coupling
to such light singlet. It is interesting that the partial width of the
invisible decay mode h\to SS by taking the upper bound value of coupling is at
a comparable level with h\to WW/ZZ or WW^(*) decay modes, making the Higgs
identifiable but with a different predicted decay BR from the standard model
Higgs decay. It will then have an impact on precision measurement of the
Higgs's properties. We also study the implication for cosmology from such a
light singlet and propose a solution to the potential problem.
