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Perturbative calculations predict that the Standard Model (SM) effectivepotential should have a new minimum, well beyond the Planck scale, much deeperthan the electroweak vacuum. As it is not obvious that gravitational effectscan get so strong to stabilize the potential, most authors have accepted themetastability scenario in a cosmological perspective. This perspective isneeded to explain why the theory remains trapped into our electroweak vacuum,but requires to control the properties of matter in the extreme conditions ofthe early universe. Alternatively, one can consider the completely differentidea of a non-perturbative effective potential which, as at the beginning ofthe SM, is restricted to the pure $\Phi^4$ sector yet consistent with the nowexisting analytical and numerical studies. In this approach, where theelectroweak vacuum is the lowest-energy state, besides the resonance of mass$m_h=125$ GeV defined by the quadratic shape of the potential at its minimum,the Higgs field should exhibit a second resonance with mass $690\pm10({\rmstat})\pm20({\rm sys})$ GeV associated with the zero-point energy determiningthe potential depth. Despite its large mass, this would couple to longitudinal$W$s with the same typical strength as the low-mass state at 125 GeV andrepresent a relatively narrow resonance of width $\Gamma_H=30\div 38$ GeV,mainly produced at LHC by gluon-gluon fusion. So it is interesting that, in theLHC data, one can find various indications for a new resonance in the expectedmass range with a non-negligible statistical significance. As this could becomean important new discovery by just adding two missing samples of RUN2 data, weoutline further refinements of the theoretical predictions that could beobtained by implementing unitarity constraints, in the presence of fermion andgauge fields, with coupled-channel calculations used for meson spectroscopy.

Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints