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

TL;DR

This paper investigates how conformal symmetry breaking, influenced by gravity and non-perturbative effects, could explain the large hierarchy between the Fermi and Planck scales through a novel instanton mechanism.

Contribution

It proposes a new non-perturbative gravitational mechanism involving instantons and non-minimal coupling to explain the Higgs scale hierarchy.

Findings

A non-perturbative gravitational effect can generate the Higgs vacuum expectation value.

The non-minimal coupling to Ricci scalar is crucial for the hierarchy.

Approximate Weyl invariance influences the mechanism's effectiveness.

Abstract

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.