Technically natural Higgs boson from Planck scale

TL;DR

This paper introduces a UV complete composite Higgs model with a Planck-scale compositeness, utilizing a novel symmetry-breaking mechanism to trigger electroweak symmetry breaking and generate fermion masses.

Contribution

It proposes a new mechanism based on softly breaking a global $\mathbb{Z}_2$ symmetry, enabling a composite Higgs model with a scale up to the Planck scale, and demonstrates it in a minimal two-Higgs scheme.

Findings

Vacuum stability analyzed via RG running of Higgs quartic coupling.

Parameter space accessible through gravitational wave signals from phase transitions.

Neutrino masses potentially generated via loops involving a second Higgs doublet.

Abstract

We propose UV complete (Partially) Composite Higgs models with compositeness scale up to the Planck scale assisted by a novel mechanism. This mechanism is based on softly breaking a global $ \mathbb{Z}_2 $ symmetry by technically natural small vacuum misalignment, dynamically triggering the electroweak symmetry breaking and Standard Model fermion mass generation. This mechanism can be present in various models based on vacuum misalignment. For concreteness, we demonstrate it in a minimal partially composite two-Higgs scheme, where the Higgs is a mixture of a composite and an elementary state, transforming odd under an $ \mathbb{Z}_2 $ symmetry. For this concrete model example, all the dimensionful fundamental parameters are approximately $ \mathcal{O}(10^{18}) $ GeV. We study the vacuum stability of this model by investigating the renormalization group running of the quartic coupling of the Higgs. Furthermore, the parameter space can already be searched by gravitational waves from a confinement-induced phase transition. Finally, the mass and mixing of the neutrinos may be naturally generated via loops of a second Higgs doublet, transforming even under the $ \mathbb{Z}_2 $ symmetry, which may be challenged by lattice calculations and a more accurate measurement of the top mass.