Hunting for the second Higgs resonance at LHC

According to perturbative calculations, the effective potential of the Standard Model should have a new minimum, well beyond the Planck scale, which is much deeper than the electroweak vacuum. Since it is not obvious that gravitational effects can become so strong to stabilize the potential, most authors have accepted the metastability scenario in a cosmological perspective. This perspective is needed to explain why the theory remains trapped into our electroweak vacuum but requires to control the properties of matter in the extreme conditions of the early Universe. As an alternative, we review the completely different idea of an effective potential which, as at the beginning of the Standard Model, is restricted to the pure phi 4 sector but is consistent with the now existing analytical and numerical studies. In this approach, where the electroweak vacuum is the lowest energy state, beside the resonance of mass mh = 125 GeV defined by the quadratic shape of the potential at its minimum, the Higgs field should exhibit a second resonance with a mass (MH)theor = 690 +/- 10 (stat) +/- 20 (sys) GeV associated with the zero-point energy which determines the potential depth. In spite of its large mass, this would couple to longitudinal W's with the same typical strength as the low-mass state at 125 GeV and represent a relatively narrow resonance of width Gamma H = 30 divided by 36 GeV, mainly produced at LHC by gluon-gluon fusion. Thus it is interesting that, in the LHC data, there are various indications for a new resonance in the expected mass range with a statistical significance which is far from being negligible and could become an important new discovery by just adding two missing samples of RUN2 data.