  Recently, conceptually new physics beyond the Standard Model has been
proposed, where a hidden conformal sector provides ``unparticle'' which couples
to the Standard Model sector through higher dimensional operators in low energy
effective theory. Among several possibilities, we focus on operators involving
unparticle, the Higgs doublet and the gauge bosons. Once the Higgs doublet
develops the vacuum expectation value, the conformal symmetry is broken and as
a result, the mixing between unparticle and Higgs boson emerges. We find that
this mixing can cause sizable shifts for the couplings between Higgs boson and
a pair of gluons and photons, because these couplings exist only at the loop
level in the Standard Model. These Higgs couplings are the most important ones
for the Higgs boson search at the CERN Large Hadron Collider, and the
unparticle physics effects may be observed together with the discovery of Higgs
boson.
