  We consider a classically conformal $U(1)$ gauge extension of the Standard
Model (SM), in which the $U(1)$ gauge symmetry is radiatively broken by the
Coleman-Weinberg mechanism. This breaking triggers the electroweak (EW)
symmetry breaking through a mixed quartic coupling between the $U(1)$ Higgs
field and the SM Higgs doublet. For two Higgs boson mass eigenstates after the
symmetry breaking, $h_1$ (SM-like Higgs boson) and $h_2$ (SM singlet-like Higgs
boson), we calculate the Higgs boson trilinear coupling ($g_{h_{1} h_{2}
h_{2}}$) in the model by setting the Higgs boson mass spectrum to be $M_{h_1} >
2 M_{h_2}$. For a common Higgs mass spectrum and mixing angle between two Higgs
fields, we find that $g_{h_{1} h_{2} h_{2}}$ in the classically conformal model
is highly suppressed compared to that calculated for the conventional Higgs
potential, where the $U(1)$ and EW symmetry breaking originate from the
negative squared masses for the Higgs fields at the tree-level. Thus, this
coupling suppression is a striking nature of the radiative origin of EW
symmetry breaking. We then consider how to distinguish this origin at the
proposed International Linear Collider (ILC) via precise measurements of
anomalous SM Higgs boson couplings and the search for anomalous SM Higgs boson
decay $h_1 \rightarrow h_2 h_2$ followed by $h_2 \to b \bar{b}$. We conclude
that once the anomalous couplings are measured at the ILC, the observation of
the anomalous Higgs boson decay is promising in the conventional Higgs
potential, while this decay process is highly suppressed and undetectable for
the classically conformal model.
