Abstract
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 asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alpha_s to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha_s (taken at 2sigma 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 scale 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.
Highlights
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
If the SM Higgs boson will be discovered at LHC in the remaining mass interval 115.5 < MH < 127 GeV not excluded at 95% [8, 9], there is no necessity for a new energy scale between the Fermi and Planck scales
If the SM Higgs boson mass will be found to coincide with Mmin given by eq (2.5), this would provide a strong argument in favor of the absence of such a scale and indicate that the electroweak symmetry breaking may be associated with the physics at the Planck scale
Summary
It will be convenient for computations to introduce yet another parameter, the “benchmark mass”, which we will call Mmin (without any superscript). MS definition of all coupling constants of the SM, fix all of them at the Fermi scale given the experimentally known parameters such as the mass of the top quark, the QCD coupling, etc., and consider the running Higgs self-coupling λ(μ) depending on the standard ’t Hooft-. Are both gauge and scheme dependent, the solution for the Higgs boson mass to these equations is gauge and scheme invariant. Where a is a common name for all the SM coupling constants (which are rather small at Planck scale), and Mi are the masses of different particles in the background of the Higgs field. The numerical evaluation for the one loop effective potential gives ∆mstability ≡ Mmstianbility − Mmin ≃ −0.15 GeV, which can be neglected in view of the uncertainties discussed below.
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