Weak scale from Planck scale -- Mass Scale Generation in Classically Conformal Two Scalar System --

Abstract

In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself can not 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 and gauge fields. In this model, due to Coleman-Weinberg-like mechanism, 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 1-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 can be verified in near future experiments.

arXiv comment41 pages, 9 figures, minor mistakes in Section VI.B and typos corrected

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