Criticality in the scale invariant standard model (squared)

Robert Foot,Archil Kobakhidze,Alexander Spencer-Smith

doi:10.1016/j.physletb.2015.05.064

Robert Foot, Archil Kobakhidze + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2015.05.064

Copy DOI

Abstract

We consider first the standard model Lagrangian with μh2 Higgs potential term set to zero. We point out that this classically scale invariant theory potentially exhibits radiative electroweak/scale symmetry breaking with very high vacuum expectation value (VEV) for the Higgs field, 〈ϕ〉≈1017–18 GeV. Furthermore, if such a vacuum were realized then cancellation of vacuum energy automatically implies that this nontrivial vacuum is degenerate with the trivial unbroken vacuum. Such a theory would therefore be critical with the Higgs self-coupling and its beta function nearly vanishing at the symmetry breaking minimum, λ(μ=〈ϕ〉)≈βλ(μ=〈ϕ〉)≈0. A phenomenologically viable model that predicts this criticality property arises if we consider two copies of the standard model Lagrangian, with exact Z2 symmetry swapping each ordinary particle with a partner. The spontaneously broken vacuum can then arise where one sector gains the high scale VEV, while the other gains the electroweak scale VEV. The low scale VEV is perturbed away from zero due to a Higgs portal coupling, or via the usual small Higgs mass terms μh2, which softly break the scale invariance. In either case, the cancellation of vacuum energy requires Mt=(171.53±0.42) GeV, which is close to its measured value of (173.34±0.76) GeV.

Highlights

Where the hμ4h part is the cosmological constant (CC) term, usually neglected as it only affects gravitational physics, e.g. [4, 5]
The Higgs quartic coupling when evolved up to a high scale ∼ 1017−18 GeV, appears to approximately satisfy: λ = λ (≡ βλ) = 0. This condition seems to be accidental, since it involves cancellation among numerically large quantitites1. We show that such a relation can naturally arise in scale invariant models as a consequence of setting the physical cosmological constant to its measured small value
We consider cases of exact classical scale invariance and the case where scale invariance is considered to be softly broken by the familiar μ2h term in the Higgs potential

Summary

Introduction

Where the hμ4h part is the cosmological constant (CC) term, usually neglected as it only affects gravitational physics, e.g. [4, 5]. In models with classical scale invariance, the CC term is absent, as required by this symmetry. We show that such a relation can naturally arise in scale invariant models as a consequence of setting the physical cosmological constant to its measured small value.

Results

Conclusion