  We study new physics effects on the couplings of weak gauge bosons with the
lightest CP-even Higgs boson ($h$), $hZZ$, and the tri-linear coupling of the
lightest Higgs boson, $hhh$, at the one loop order, as predicted by the two
Higgs doublet model. Those renormalized coupling constants can deviate from the
Standard Model (SM) predictions due to two distinct origins; the tree level
mixing effect of Higgs bosons and the quantum effect of additional particles in
loop diagrams. The latter can be enhanced in the renormalized $hhh$ coupling
constant when the additional particles show the non-decoupling property.
Therefore, even in the case where the $hZZ$ coupling is close to the SM value,
deviation in the $hhh$ coupling from the SM value can become as large as plus
100 percent, while that in the $hZZ$ coupling is at most minus 1 percent level.
Such large quantum effect on the Higgs tri-linear coupling is distinguishable
from the tree level mixing effect, and is expected to be detectable at a future
linear collider.
