Spontaneous Symmetry Breaking and Its Pattern of Scales

Spontaneous Symmetry Breaking (SSB) in lambda phi 4 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 Mh2 similar to mh2ln(?s/Mh), where ?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 similar to 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.