Dilaton-assisted generation of the Fermi scale from the Planck scale

In scale-invariant theories of gravity the Planck mass $M_P$, which appears due to spontaneous symmetry breaking, can be the only scale at the classical level. It was argued that the second scale can be generated by a quantum non-perturbative gravitational effect. The new scale, associated with the Higgs vacuum expectation value, can be orders of magnitude below $M_P$, leading to the hierarchy between the Fermi and the Planck scales. We study a theory in which the non-perturbative effect is sensitive both to the physics at energy scales as high as $M_P$ and to the low-energy, Standard Model physics. This makes it possible to constrain the mechanism from experiment. We find that the crucial ingredients of the mechanism are non-minimal coupling of the scalar fields to gravity, the approximate Weyl invariance at high energies, and the metastability of the low-energy vacuum.