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

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 nonperturbative 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.

Einstein-Cartan gravity, matter, and scale-invariant generalization

“…Higgs inflation, but it can also host the non-perturbative gravitational mechanism of Electroweak symmetry breaking suggested in [57] and studied further in [58][59][60]. Once all particles of the Standard Model are included, however, the Palatini formulation of gravity is no longer appropriate.…”

Vacuum decay and quadratic gravity: the massive case

“…Quantum tunnelling through an energy barrier has an exponentially small probability to occur in the semi-classical approximation. The smallness of some numbers, for example the ratio among the Higgs vacuum expectation value and the Planck mass, may be viewed in these terms (thus alleviating the hierarchy problem [39][40][41][42][43]), as…”

“…The singularity drives W to infinity. It has been shown that a possible way to make it finite is to add higher order kinetic terms (∂ψ) n , n > 2, to the Lagrangian [39][40][41][42][43]. Another application of higher-derivative terms to solve the hierarchy problem is addressed in [55] regarding the agravity theory [56].…”

“…We also overlooked derivative self-interactions and scalar field decay in a number of space dimensions d other than three. The former has been found to be a candidate high-energy correction to solve the hierarchy problem [39][40][41][42][43]. The latter might be relevant as there are recent proposals for analogue experiments with d < 3 [44][45][46][47][48][49][50].…”

Aspects of spontaneous breaking of conformal invariance in the Fishnet CFT

“…Note that the latter theories may provide the appropriate language to address yet another fine-tuning puzzle of the Standard Model: the gauge hierarchy problem. It has been argued that the smallness of the Higgs mass as compared to the Planck scale may be the consequence of scale/conformal symmetry [62,32] in combination with no particle thresholds between the electroweak and Planck scales [63,27], 3 and the presence of nonperturbative gravitational effects operative at very high energies [65][66][67][68].…”