The mass scales of the Higgs field

Abstract

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 [Formula: see text] theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: (i) a lower mass [Formula: see text], defined by its quadratic shape at the minima, and (ii) a larger mass [Formula: see text], defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by [Formula: see text], where [Formula: see text] 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 [Formula: see text] and [Formula: see text] are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. [Formula: see text] GeV, to a much larger [Formula: see text]. The same lattice data give a final estimate [Formula: see text] GeV which induces to reconsider the experimental situation at Large Hadron Collider (LHC). In particular an independent analysis of the ATLAS[Formula: see text]+[Formula: see text]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.