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. arXiv:1804.06376v2 [hep-th] 5 Oct 2018 ContentsRegardless the particular content of a model extending the SM at high energies, a common approach to the hierarchy problem lies within the effective field theory framework. The latter implies that the low energy description of Nature, provided by the SM, can be affected by an unknown UV physics only through a finite set of parameters. Two of them -the mass of the Higgs boson and the cosmological constant -are most sensitive to the scale and to the dynamics of physics beyond the SM, being quadratically and quartically divergent. In "natural" theories the quadratically divergent UV contributions to the Higgs mass are eliminated by introducing new physics right above the Fermi scale. It is this naturalness principle that is seriously questioned now in light of the absence of signatures of new physics at the TeV scale [10]. While some parameter regions of the theories with M X ∼ 1 TeV still survive at the price of a moderate fine-tuning, a relatively radical step would be to suggest that the UV physics can affect the low energy behavior in a way that is not captured by the perturbation theory. Going back to the ratio (1.1), this would imply the existence of a non-perturbative effect linking the scales separated by 17 orders of magnitude.The idea of some principle that can shape the behavior of a theory at very different energy scales is not novel to particle physics. For example, it is tempting to use such kind of reasoning when investigating a probable (near-)degeneracy of the minima of the Renormalization Group (RG) improved SM Higgs potential, which is supported by the recent measurements of the Higgs and top quark masses [22,23]. A possible mechanism that makes the form of the potential special and, hence, predicts the values of the low energy parameters, can manifest itself in a number of ways. For example, in [24] bounds on the Higgs and top quark masses were put based on the principle of multiple point criticality [25], while in [26] the prediction of m H was made, guiding by an asymptotic safety of gravity [27]. Inspired by these ideas, in this paper we make an attempt to resolve the problem (1.1) by looking for an inherently non-perturbative effect relati...

We study quantum effects in Higgs inflation in the Palatini formulation of gravity, in which the metric and connection are treated as independent variables. We exploit the fact that the cutoff, above which perturbation theory breaks down, is higher than the scale of inflation. Unless new physics above the cutoff leads to unnaturally large corrections, we can directly connect low-energy physics and inflation. On the one hand, the lower bound on the top Yukawa coupling due to collider experiments leads to an upper bound on the non-minimal coupling of the Higgs field to gravity: ξ 10 8 . On the other hand, the Higgs potential can only support successful inflation if ξ 10 6 . This leads to a fairly strict upper bound on the top Yukawa coupling of 0.925 (defined in the MS-scheme at the energy scale 173.2 GeV) and constrains the inflationary prediction for the tensor-to-scalar ratio. Additionally, we compare our findings to metric Higgs inflation.

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 ∼ Λ QCD ∼ 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 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 nonminimal 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.