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If the mass of the Higgs boson is put to zero, the classical Lagrangian ofthe Standard Model (SM) becomes conformally invariant (CI). Taking into accountquantum non-perturbative QCD effects violating CI leads to electroweak symmetrybreaking with the scale $v \sim \Lambda_{\rm QCD}\sim 100$ MeV which is threeorders of magnitude less than it is observed experimentally. Depending on themass of the top quark, the radiative corrections may lead to another minimum ofthe 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. Wesuggest a non-perturbative mechanism that can reproduce the observed hierarchybetween the Fermi and the Planck scales, by constructing an instantonconfiguration contributing to the vacuum expectation value of the Higgs field.The crucial role in this effect is played by the non-minimal coupling of theHiggs field to the Ricci scalar and by the approximate Weyl invariance of thetheory for large values of the Higgs field.

Conformal symmetry: towards the link between the Fermi and the Planck scales