Abstract
The Higgs naturalness problem is solved if the growth of Einstein's gravitational interaction is softened at an energy $ \lesssim 10^{11}\,$GeV (softened gravity). We work here within an explicit realization where the Einstein-Hilbert Lagrangian is extended to include terms quadratic in the curvature and a non-minimal coupling with the Higgs. We show that this solution is preserved by adding three right-handed neutrinos with masses below the electroweak scale, accounting for neutrino oscillations, dark matter and the baryon asymmetry. The smallness of the right-handed neutrino masses (compared to the Planck scale) and the QCD $\theta$-term are also shown to be natural. We prove that a possible gravitational source of CP violation cannot spoil the model, thanks to the presence of right-handed neutrinos. Inflation is approximately described by the Starobinsky model in this context, and can occur even if we live in a metastable vacuum.
Highlights
The hierarchy problem consists in finding an extension of the Standard Model (SM) where the Higgs mass Mh is natural: quantum corrections to Mh are small compared to its observed value
An important question is whether this scenario can be made realistic and can address the shortcomings of the SM: nonzero neutrino masses, dark matter (DM), baryon asymmetry of the Universe (BAU), inflation as well as an explication for the smallness of the QCD θ-term
Theories of this sort are sensible as long as we only look at the energy spectrum and transition probabilities between asymptotic states (S-matrix elements)
Summary
The hierarchy problem consists in finding an extension of the Standard Model (SM) where the Higgs mass Mh is natural: quantum corrections to Mh are small compared to its observed value. Softened gravity is a scenario in which the growth of Einstein’s gravitational interaction stops at a scale no larger than 1011 GeV [1] In such a situation, the gravitational quantum corrections to Mh are not too large solving the hierarchy problem. Inflation is mainly due to the effective Starobinsky scalar z [7] (which automatically emerges from the terms quadratic in the curvature), and the Higgs gives very small contributions even in the natural parameter space. We find it remarkable that all the above-mentioned problems can be solved in such a simple extension of the SM.
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