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

## TL;DR

This paper explores a scale-invariant gravity theory where a quantum gravitational effect generates the Fermi scale from the Planck scale, linking high-energy physics with low-energy phenomena and constraining the hierarchy problem.

## Contribution

It introduces a model where non-perturbative gravitational effects, coupled with Weyl invariance and scalar fields, generate the Fermi scale from the Planck scale, with potential experimental implications.

## Key findings

- The Fermi scale can arise from quantum gravitational effects.
- Non-minimal scalar-gravity coupling is essential for the mechanism.
- The model predicts observable consequences related to vacuum metastability.

## Abstract

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.