Multi-step phase transition and gravitational wave from general $\mathbb{Z}_2$ scalar extensions

TL;DR

This paper explores multi-step phase transitions in a standard model extension with an isospin scalar, highlighting conditions for first-order transitions and the potential for detectable gravitational waves.

Contribution

It analyzes the dynamics of multi-step phase transitions with an isospin scalar under a Z2 symmetry, identifying conditions for first-order transitions and gravitational wave production.

Findings

Multi-step phase transition can be triggered with moderate Higgs-scalar coupling.

First-order transition at the first step is driven by thermal loop effects.

Detectable gravitational waves are likely from the second step.

Abstract

Multi-step phase transition provides a paradigm in which a broken symmetry during phase transition can be restored, enriching the phenomena of both dark matter and baryon asymmetry. We study the dynamics of the multi-step phase transition in the standard model extension with additional isospin $N$-plet scalar field $\Phi_2$ under a discrete $\mathbb{Z}_2$ symmetry. We find that the multi-step phase transition could be triggered if there is a moderately large coupling between the Higgs and the $\Phi_2$ and this coupling is required to be larger as the mass of the $\Phi_2$ and/or isospin increase. The first-order phase transition at the first (second) step can be realized by the thermal loop (tree-level barrier) effects. Thus it is more likely that a detectable spectrum of gravitational waves can be produced at the second step of the phase transition.