The Higgs condensate as a quantum liquid: A critical comparison with observations

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper we compare the triviality scenario and the renormalised two-loop perturbation theory to precise and extensive results from non-perturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalised perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behave like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes $H \rightarrow WW$, while in the preliminary Run 2 data there are hints of the decays $H \rightarrow ZZ$ in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.