  Quantum corrections generate a quadratically divergent mass term for the
Higgs boson in the Standard Model. Thus, if the Higgs boson has a mass of order
100 GeV, it implies the presence of a cut-off of the theory around TeV scale,
and some particles associated with the new physics may appear around the
cut-off scale $\Lambda$. However, if $\Lambda$ is several TeV, it may be
difficult to find such particles at the LHC. In this paper, we consider a
situation in which the new physics provides relatively light particles compared
with the scale $\Lambda$. In such a situation, we show that diphoton event and
four lepton event by the decay of the Higgs and/or a new particle have
naturally large cross section, and LHC may test the new physics in a
considerably broad parameter region even if $\Lambda$ is several TeV.
