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 non-perturbative 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.
Highlights
AND SETUPIn the Standard Model (SM), the Higgs mass mH is the only scale at the classical level
We demonstrate the sensitivity of this mechanism to the low-energy physics that shapes the instanton profile far from its core region
Let us summarize our findings and outline the features of the nonperturbative mechanism of generation of a new scale, the ones which are specific to the model (6), and the ones which this model has in common with the theories studied previously in [25,26]
Summary
In the Standard Model (SM), the Higgs mass mH is the only scale at the classical level. If the physics beyond the Standard Model (BSM) contains new heavy d.o.f., it is, in general, a source of large perturbative corrections to the Higgs mass; for overviews of the problem see [12,13]. The two regions of energy scales at which the action is saturated can be separated by many orders of magnitude This happens due to a peculiar behavior of the instanton profile, namely, due to the fact that the profile is not a monotonic function of the distance from the center of the configuration. We use similar arguments and employ the same type of UV operators to eliminate the divergence of the solution at the source point and to generate the large high-energy contribution BHE.
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