In the first version of the theory, with a classical scalar potential, the sector inducing SSB was distinct from the Higgs field interactions induced through its gauge and Yukawa couplings. We have adopted a similar perspective but, following most recent lattice simulations, described SSB in $lambdaPhi^4$ theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: i) a lower mass $m_h$, defined by its quadratic shape at the minima, ~and~ ii) a larger mass $M_h$, defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by $M^2_hsim m^2_h ln (Lambda_s/M_h)$, where $Lambda_s$ is the ultraviolet cutoff of the scalar sector. We have checked this two-scale structure with lattice simulations of the propagator and of the susceptibility in the 4D Ising limit of the theory. These indicate that, in a cutoff theory where both $m_h$ and $M_h$ are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. $m_h$=125 GeV, to a much larger $M_h$. The same lattice data give a final estimate $M_h= 720 pm 30 $ GeV which induces to re-consider the experimental situation at LHC. In particular an independent analysis of the ATLAS + CMS data indicating an excess in the 4-lepton channel as if there were a new scalar resonance around 700 GeV. Finally, the presence of two vastly different mass scales, requiring an interpolating form for the Higgs field propagator also in loop corrections, could reduce the discrepancy with those precise measurements which still favor large values of the Higgs particle mass.
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