Criticality in the scale invariant standard model (squared)

TL;DR

This paper explores a classically scale-invariant extension of the Standard Model with two sectors, predicting a critical Higgs self-coupling and a high-scale vacuum, and relates vacuum energy cancellation to the top quark mass.

Contribution

It introduces a two-sector Standard Model extension with exact Z2 symmetry that predicts criticality and high-scale symmetry breaking, connecting vacuum energy cancellation to the top quark mass.

Findings

Predicts a high-scale Higgs vacuum expectation value (~10^{17-18} GeV)

Shows the model's vacuum energy cancellation constrains the top quark mass to ~171.5 GeV

Demonstrates near vanishing Higgs self-coupling and beta function at the critical point

Abstract

We consider first the standard model Lagrangian with $\mu_h^2$ Higgs potential term set to zero. We point out that this clasically scale invariant theory potentially exhibits radiative electroweak/scale symmetry breaking with very high vacuum expectation value (VEV) for the Higgs field, $< \phi > \approx 10^{17-18}$ 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, $\lambda (\mu=< \phi >)\approx \beta_{\lambda} (\mu=< \phi >)\approx 0$. A phenomenologically viable model that predicts this criticality property arises if we consider two copies of the standard model Lagrangian, with exact $Z_2$ 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 $\mu_h^2$, which softly break the scale invariance. In either case, the cancellation of vacuum energy requires $M_t = (171.53 \pm 0.42)$ GeV, which is close to its measured value of $(173.34 \pm 0.76)$ GeV.