In response to the 2013 Update of the European Strategy for Particle Physics, the Future Circular Collider (FCC) study was launched, as an international collaboration hosted by CERN. This study...

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by...

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 α _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 1–2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and α _s (taken at the 2σ level) the bound reads M _H ≥ M _min (equality corresponds to the asymptotic-safety prediction), where \( {{M}_{{\min }}}=\left( {129\pm 6} \right) \) 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 ~ (200 + 200 GeV) (Higgs and t-quark factory) would be needed.

We perform a manifestly gauge-independent analysis of the vacuum stability in the standard model including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the Higgs self-coupling and its beta function in the modified minimal-subtraction scheme and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the standard model be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with the Monte Carlo mass quoted by the Particle Data Group at the $1.3\sigma$ level.