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 λΦ4 theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: (i) a lower mass mh, defined by its quadratic shape at the minima, and (ii) a larger mass Mh, defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by M2h∼m2hln(Λs/Mh), where Λs 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 mh and Mh are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. mh=125 GeV, to a much larger Mh. The same lattice data give a final estimate Mh=720±30 GeV which induces to reconsider the experimental situation at Large Hadron Collider (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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