Asymptotic safety of gravity and the Higgs boson mass

There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson mH can be predicted. For a positive gravity induced anomalous dimension Aλ>0 the running of the quartic scalar self interaction λ at scales beyond the Planck mass is determined by a fixed point at zero. This results in mH=mmin=126 GeV, with only a few GeV uncertainty. This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For Aλ<0 one finds mH in the interval mmin0 is favored by explicit computations existing in the literature.