Higgs boson mass and new physics

We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from the asymptotic safety of the SM. We account for the three-loop renormalization group evolution of the couplings of the SM and for a part of the two-loop corrections that involve the QCD coupling alpha(s) to the initial conditions for their running. This is one step beyond the current state-of-the-art procedure ("one-loop matching-two-loop running"). This results in a reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the SM physics, to 1-2GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha(s) (taken at the 2 sigma level) the bound reads M-H >= M-min (equality corresponds to the asymptotic-safety prediction), where M-min = (129 +/- 6) GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of M-H with M-min would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scales a construction of an electron-positron or muon collider with a center-of-mass energy similar to (200 + 200 GeV) (Higgs and t-quark factory) would be needed.