Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

Hikaru Kawai,Junichi Haruna

doi:10.1093/ptep/ptz165

Hikaru Kawai, Junichi Haruna

Open Access

https://doi.org/10.1093/ptep/ptz165

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Abstract

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

Highlights

The mass of the Higgs particle in the standard model is the only parameter with mass dimensions, which determines the masses of all particles except for the quantum chromodynamics scale
Because supersymmetry particles have not been found in recent accelerator experiments such as LHC, the possibility that the standard model is an effective theory up to the Planck scale has become more realistic except for some small corrections [1,2,3]
We couple the classically conformal Z2 × Z2 invariant two-scalar model with the standard model and investigate whether the mechanism examined in Sect. 3 can be used as a mechanism to generate the weak scale from the Planck scale

Summary

Introduction

The mass of the Higgs particle in the standard model is the only parameter with mass dimensions, which determines the masses of all particles except for the quantum chromodynamics scale. Unlike the case of the simple φ 4 model, we observe that this vacuum expectation value does not disappear even if the effective potential is improved by the renormalization group. We calculate the effective potential and see that it looks like a vacuum expectation value is generated through the Coleman–Weinberg mechanism. By improving it by the renormalization group, we see that this is an error. We calculate the effective potential of the O(N ) × O(N ) scalar model, corresponding to the model, exactly in the large-N limit, and show that only one of the scalar fields has a nonzero vacuum expectation value.

Two-scalar model as Higgs portal dark matter

Conclusion