  If the mass of the Higgs boson is put to zero, the classical Lagrangian of
the Standard Model (SM) becomes conformally invariant (CI). Taking into account
quantum non-perturbative QCD effects violating CI leads to electroweak symmetry
breaking with the scale $v \sim \Lambda_{\rm QCD}\sim 100$ MeV which is three
orders of magnitude less than it is observed experimentally. Depending on the
mass of the top quark, the radiative corrections may lead to another minimum of
the effective potential for the Higgs field with $v \gtrsim M_P$, where $M_P$
is the Planck mass, at least $16$ orders of magnitude more than it is observed.
We explore yet another source of CI breaking associated with gravity. We
suggest a non-perturbative mechanism that can reproduce the observed hierarchy
between the Fermi and the Planck scales, by constructing an instanton
configuration contributing to the vacuum expectation value of the Higgs field.
The crucial role in this effect is played by the non-minimal coupling of the
Higgs field to the Ricci scalar and by the approximate Weyl invariance of the
theory for large values of the Higgs field.
