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

Abstract Perturbative calculations predict that 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. So far, most authors have accepted the metastability scenario in a cosmological perspective which is needed to explain why the theory remains trapped in our electroweak vacuum but requires to control the properties of matter in the extreme conditions of the early universe. As an alternative, one can consider the completely different idea of a non-perturbative effective potential that, as at the beginning of the Standard Model, is restricted to the pure $$\Phi ^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>Φ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> sector but is consistent with the indications of the now existing analytical and numerical studies, namely “triviality” and a description of SSB as weak first-order phase transition. In this approach, the electroweak vacuum is now the lowest energy state because, besides the state with mass $$m_h=125$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>h</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>125</mml:mn> </mml:mrow> </mml:math> GeV, defined by the quadratic shape of the potential at its minimum, there is a second much larger mass scale $$(M_H)^\textrm{Theor} \sim 690(30)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext>Theor</mml:mtext> </mml:msup> <mml:mo>∼</mml:mo> <mml:mn>690</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>30</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> GeV associated with the zero-point energy determining the potential depth. Despite its large mass, the heavier state would couple to longitudinal W s with the same typical strength as the low-mass state at 125 GeV and thus represent a relatively narrow resonance mainly produced at LHC by gluon-gluon fusion. Therefore, it is interesting that, in the LHC data, one can find combined indications of a new resonance of mass $$(M_H)^\textrm{comb} \sim 685 (10)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mtext>comb</mml:mtext> </mml:msup> <mml:mo>∼</mml:mo> <mml:mn>685</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>10</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> GeV, with a statistical significance which is far from negligible. Since this non-negligible evidence could become an important new discovery with forthcoming data, we outline further refinements of the theoretical predictions, that could be obtained by implementing unitarity constraints, in the presence of fermion and gauge fields, with the type of coupled-channel calculations nowadays used in meson spectroscopy.