Based on a scenario for asymptotic safety for gravity the Higgs boson mass was predicted in 2009 to be 126 GeV, with a few GeV uncertainty. We review this proposal and its implications for a desert between the Fermi- and Planck- scales, the possible solutions to the gauge hierarchy problem and the unification of all interactions.
An observed mass of the Higgs boson close to 126 GeV suggests a solution of the hierarchy problem at a unification scale close to the Planck mass. It also points to the possibility that the physics beyond the standard model needed for dark energy, dark matter, baryon asymmetry, neutrino masses and inflation may be characterized by very high energy scales or extremely small couplings, and not be accessible to laboratory experiments.
A crucial ingredient for the robustness of the prediction of the Higgs boson mass is the existence of a partial infrared fixed point for the ratio between squared Yukawa coupling of the top quark and quartic scalar coupling, and the properties of the associated infrared interval.
