# Electro-weak Phase Transition With Three Phases in The $SU(2)_1 \otimes SU(2)_2 \otimes U(1)_Y$ Model

## TL;DR

This paper investigates a three-phase electroweak phase transition in an extended gauge model, finding it to be first-order at 200 GeV with implications for gauge symmetry breaking and new particle masses.

## Contribution

It demonstrates that the $SU(2)_1 imes SU(2)_2 imes U(1)_Y$ model exhibits a first-order electroweak phase transition at the SM scale, providing constraints on model parameters.

## Key findings

- First-order EWPT occurs at 200 GeV in the model.
- The phase transition strength ranges from 1 to 2.7.
- New gauge bosons have masses above 1.7 TeV.

## Abstract

Our analysis shows that SM-like electroweak phase transition (EWPT) in the $SU(2)_1 \otimes SU(2)_2 \otimes U(1)_Y$ (2-2-1) model is a first-order phase transition at the $200$ GeV scale (the SM scale). Its strength ($S$) is about $1 - 2.7$ and the masses of new gauge bosons are larger than $1.7$ TeV when the second VEV is larger than $535$ GeV in a three-stage EWPT scenario and the coupling constant of $SU(2)_2$ group must be larger than 2. Therefore, this first order EWPT can be used to fix VEVs and the coupling constant of the gauge group in electro-weak models.