  The recent discovery of the Higgs-like particle at around 126 GeV has given
us a big hint towards the origin of the Higgs potential. Especially the running
quartic coupling vanishes near the Planck scale, which indicates a possible
link between the physics in the electroweak and the Planck scales. Motivated by
this and the hierarchy problem, we investigate a possibility that the Higgs has
a flat potential at the Planck scale. In particular, we study the RG analysis
of the B-L extension of the standard model with a classical conformality. The
B-L symmetry is radiatively broken at the TeV scale via the Coleman-Weinberg
mechanism. The electroweak symmetry breaking is triggered by a radiatively
generated scalar mixing so that its scale 246 GeV is dynamically related with
the B-L breaking scale at TeV. The Higgs boson mass is given at the border of
the stability bound,which is lowered by a few GeV from the SM by the effect of
the B-L gauge interaction.
