*Article* **Spontaneous Symmetry Breaking and Its Pattern of Scales**

#### **Maurizio Consoli 1 and Leonardo Cosmai 2,\***


Received: 12 November 2020; Accepted: 4 December 2020; Published: 9 December 2020

**Abstract:** Spontaneous Symmetry Breaking (SSB) in *λ*Φ<sup>4</sup> theories is usually described as a 2nd-order phase transition. However, most recent lattice calculations indicate instead a weakly 1st-order phase transition as in the one-loop and Gaussian approximations to the effective potential. This modest change has non-trivial implications. In fact, in these schemes, the effective potential at the minima has two distinct mass scales: (i) a first mass *mh* associated with its quadratic curvature and (ii) a second mass *Mh* associated with the zero-point energy which determines its depth. The two masses describe different momentum regions in the scalar propagator and turn out to be related by *<sup>M</sup>*2*h* ∼ *m*2*h* ln(<sup>Λ</sup>*s*/*Mh*), where Λ*s* is the ultraviolet cutoff of the scalar sector. Our lattice simulations of the propagator are consistent with this two-mass picture and, in the Standard Model, point to a value *Mh* ∼ 700 GeV. However, despite its rather large mass, this heavier excitation would interact with longitudinal W's and Z's with the same typical coupling of the lower-mass state and would therefore represent a rather narrow resonance. Two main novel implications are emphasized in this paper: (1) since vacuum stability depends on the much larger *Mh*, and not on *mh*, SSB could originate within the pure scalar sector regardless of the other parameters of the theory (e.g., the vector-boson and top-quark mass) (2) if the smaller mass were fixed at the value *mh* =125 GeV measured at LHC, the hypothetical heavier state *Mh* would then naturally fit with the peak in the 4-lepton final state observed by the ATLAS Collaboration at 700 GeV.

**Keywords:** Spontaneous Symmetry Breaking; BEH field mass spectrum; LHC experiments

**PACS:** 11.30.Qc; 12.15.-y; 13.85.-t
