Electroweak vacuum stability in the Higgs-Dilaton theory

We study the stability of the Electroweak (EW) vacuum in a scale-invariant extension of the Standard Model and General Relativity, known as a Higgs-Dilaton theory. The safety of the EW vacuum against possible transition towards another vacuum is a necessary condition for the model to be phenomenologically acceptable. We find that, within a wide range of parameters of the theory, the decay rate is significantly suppressed compared to that of the Standard Model. We also discuss properties of a tunneling solution that are specific to the Higgs-Dilaton theory.Comment: 16 pages, 5 figure

Gravity, Scale Invariance and the Hierarchy Problem

Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We argue that this hierarchy can be generated by a non-perturbative effect relating the low energy and the Planck-scale physics. The effect is manifested in the existence of an instanton configuration contributing to the vacuum expectation value of the Higgs field. We analyze such configurations in several toy models and in a phenomenologically viable theory encompassing the Standard Model and General Relativity in a scale-invariant way. Dynamical gravity and a non-minimal coupling of it to the Higgs field play a crucial role in the mechanism.Comment: 42 pages, 11 figures. v2: published versio

Q-holes

We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that describe dips or rises in the spatially-uniform charge distribution. We also present explicit analytical solutions for some of such objects and examine their properties.Comment: 17 pages, 11 figures, LaTeX. v3: minor corrections in the tex

Out of this world neutrino oscillations

We study how vacuum neutrino oscillations can be affected by a causal, nonlinear and state-dependent modification of quantum field theory that may be interpreted using the many-worlds formulation of quantum mechanics. The effect is induced by a Higgs-neutrino Yukawa interaction that causes a nonlinear interference between the neutrino mass eigenstates. This leads to a tiny change in the oscillation pattern of light, active neutrinos without altering the oscillation frequencies. At large baselines where the oscillations disappear, the nonlinear effect is also suppressed and does not source correlations between the mass eigenstates once they are entangled with the environment. Our example provides a way to compute effects of nonlinear quantum mechanics and field theory that may probe the possible physical reality of many worlds.Comment: 9 pages, 1 figure. v2: version published in PR

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 $v \sim \Lambda_{\rm QCD}\sim 100$ 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.Comment: 12 pages, 6 figures; v2: published versio