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

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 $v\sim {\Lambda }_{\mathrm{QCD}}\sim 100$ 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.

12 pages, 6 figures; v2: published version

References in corpus (11)

• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Higgs inflation: consistency and generalisations
• Power-counting and the Validity of the Classical Approximation During Inflation
• Conformal Symmetry and the Standard Model
• Quantum scale invariance, cosmological constant and hierarchy problem
• Scale invariance, unimodular gravity and dark energy
• A Clockwork Theory
• Why should we care about the top quark Yukawa coupling?
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Is there a new physics between electroweak and Planck scales?
• Recent Top Quark Mass Measurements from CMS

Cited by in corpus (22)

• Exact Correlation Functions in Conformal Fishnet Theory
• Higgs inflation in Einstein-Cartan gravity
• Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Einstein-Cartan Portal to Dark Matter
• Matter matters in Einstein-Cartan gravity
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Gravity, Scale Invariance and the Hierarchy Problem
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Scale-invariant alternatives to general relativity. III. The inflation--dark-energy connection
• One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry
• Asymptotic Scale Invariance and its Consequences
• Dilaton-assisted generation of the Fermi scale from the Planck scale
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• Anomaly-free scale symmetry and gravity
• Higgs field in cosmology
• Consistent Conformal Extensions of the Standard Model
• QFT without infinities and hierarchy problem
• Higgs-dilaton model revisited: can dilaton act as QCD axion?
• Vacuum decay and quadratic gravity: the massive case
• Higgs-Dilaton Inflation in Einstein-Cartan gravity