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

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 similar to Lambda(QCD) similar to 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 greater than or similar to 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. (c) 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).

Euclidean classical solutions in quantum field theory and gravity: Higgs vacuum metastability and the hierarchy problem

Andrey Shkerin

The thesis is dedicated to two groups of questions arising in modern particle physics and cosmology. The first group concerns with the problem of stability of the electroweak (EW) vacuum in different environments. Due to its phenomenological significance, the problem attracts high attention in recent research. We contribute to this research in two directions. First, we study decay rate of the EW vacuum at the inflationary stage of the universe. While in a low density, low temperature environment characteristic of the present-day universe the Standard Model EW vacuum is safely long-lived, the situation may be different during inflation. We estimate tunneling transition via Coleman-De Luccia instanton in this case and confirm that it is exponentially suppressed, contrary to the claims made in the literature. Second, we compute the lifetime of the EW vacuum in a scale-invariant extension of the Standard Model and gravity, known as the Higgs-Dilaton theory. The theory passes phenomenological tests and provides us with a plausible cosmological scenario. To confirm its viability, it is necessary to check if the EW vacuum in this theory is sufficiently safe. We perform this check and find that features of the Higgs-Dilaton theory yield additional stabilization of the low-energy vacuum, compared to the Standard Model case. Another group of questions addressed in the thesis is related to the hierarchy problem. Combining quantum scale invariance with the absence of new degrees of freedom above the EW scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We suggest that this hierarchy can be a manifestation of a non-perturbative effect relating low-energy and strong-gravity domains of the theory. To support this suggestion, we construct instanton configurations and investigate their contribution to the vacuum expectation value of the Higgs field. The effect we find relies on properties of the theory in the ultraviolet regime. Non-minimal coupling of the Higgs field to the Ricci scalar and an approximate Weyl invariance of the theory in this regime are important ingredients of the mechanism. Dynamical gravity plays a crucial role in the effect as it leads to existence of instanton solutions suitable for generating the EW scale.

EPFL2018

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

Andrey Shkerin

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 nonperturbative 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.

AMER PHYSICAL SOC2019

Euclidean classical solutions in quantum field theory and gravity: Higgs vacuum metastability and the hierarchy problem

Andrey Shkerin

EPFL2018