  If the LHC does only find a Higgs boson in the low mass region and no other
new physics, then one should reconsider scenarios where the Standard Model with
three right-handed neutrinos is valid up to Planck scale. We assume in this
spirit that the Standard Model couplings are remnants of quantum gravity which
implies certain generic boundary conditions for the Higgs quartic coupling at
Planck scale. This leads to Higgs mass predictions at the electroweak scale via
renormalization group equations. We find that several physically well motivated
conditions yield a range of Higgs masses from 127-142 GeV. We also argue that a
random quartic Higgs coupling at the Planck scale favors M_H > 150 GeV, which
is clearly excluded. We discuss also the prospects for differentiating
different boundary conditions imposed for \lambda(M_{pl}) at the LHC. A
striking example is M_H = 127\pm 5 GeV corresponding to \lambda(M_{pl})=0,
which would imply that the quartic Higgs coupling at the electroweak scale is
entirely radiatively generated.
