Naturalizing Gravity of the Quantum Fields, and the Hierarchy Problem

Abstract

It is shown that gravity can be incorporated into the Standard Model (SM) in a way solving the hierarchy problem. For this, the SM effective action in flat spacetime is adapted to curved spacetime via not only the general covariance but also the gauge invariance. For the latter, gauge field hard masses, induced by loops at the UV scale $\Lambda$, are dispelled by construing $\Lambda$ as the constant value assigned to curvature. This gives way to an unprecedented mechanism for incorporating gravity into the SM in that the hierarchy problem is solved by transmutation of the Higgs boson $\Lambda^2$--mass into the Higgs-curvature coupling, and the cosmological constant problem is alleviated by metamorphosis of the vacuum $\Lambda^4$--energy into the Einstein-Hilbert term. Gravity emerges correctly if the SM is accompanied by a secluded dark sector sourcing non-interacting dark matter, dark energy and dark radiation. Physics beyond the SM, containing Higgs-phobic scalars that resolve the strong CP problem, flavor problem, baryogenesis and inflation, respects the hierarchy. Majorana neutrinos are naturally incorporated if $\Lambda$ lies at the see-saw scale. This mechanism, in general, leaves no compelling reason to anticipate new particles at the LHC or higher-energy colliders.