Spontaneous Symmetry Breaking and Its Pattern of Scales

Maurizio Consoli,Leonardo Cosmai

doi:10.3390/sym12122037

Maurizio Consoli, Leonardo Cosmai

Open Access

https://doi.org/10.3390/sym12122037

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Abstract

Spontaneous Symmetry Breaking (SSB) in λΦ4 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∼mh2ln(Λs/Mh), where Λs 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.

Highlights

Spontaneous Symmetry Breaking (SSB) through the vacuum expectation value hΦi 6= 0 of a fundamental scalar field, the BEH field [1,2], is an essential element of the Standard Model
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 (2) if the smaller mass were fixed at the value mh =125 GeV measured at LHC, the hypothetical heavier state Mh would naturally fit with the peak in the 4-lepton final state observed by the ATLAS Collaboration at 700 GeV
This original idea has been recently confirmed by the discovery at LHC [3,4] of a narrow scalar resonance with mass mh ∼ 125 GeV whose characteristics fit well with the theoretical expectations

Summary

Introduction

Spontaneous Symmetry Breaking (SSB) through the vacuum expectation value hΦi 6= 0 of a fundamental scalar field, the BEH field [1,2], is an essential element of the Standard Model. VGauss ( φ = 0) = 0, the Gaussian effective potential for the O(2) and O(N)-symmetric scalar theories exhibits SSB again supporting the weak 1st-order picture It was noted the non-uniformity of the two limits N → ∞ and ultraviolet cutoff Λs → ∞. To fully appreciate the substantial equivalence with the one-loop potential, we observe that the infinite additional terms in the Gaussian effective potential can be expressed in a form analogous to Equation (5) with a simple redefinition of the classical background and of the φ−dependent mass in the zero-point energy, i.e., Ω4 ( φ ). Since the above arguments (i) and (ii) confirm the 1st-order picture of SSB, and the general validity of the 1-loop and Gaussian approximations to the effective potential, we will consider in Section 3 some important physical implications of this scenario

Two-Mass Scales in the Broken Phase

Observable Interactions for a Large Mh

Some Predictions for the LHC Experiments