Symmetry breaking patterns of the 3-3-1 model at finite temperature

TL;DR

This paper investigates the symmetry breaking patterns and phase transitions in the minimal 3-3-1 extension of the standard model at finite temperature, revealing two first-order transitions and a potentially weak electroweak transition.

Contribution

It provides a detailed analysis of the symmetry breaking and phase transition patterns in the 3-3-1 model, including the conditions for first-order transitions at finite temperature.

Findings

Identifies two first-order phase transitions in the 3-3-1 model.

Finds the electroweak transition to be very weak, possibly second-order.

Determines critical temperatures for symmetry restoration.

Abstract

We consider the minimal version of an extension of the standard electroweak model based on the $SU(3)_c \times SU(3)_L \times U(1)_X$ gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of $SU(3)_L$, whose neutral components develop nonzero vacuum expectation values, giving mass for all the model's massive particles. {}For different choices of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L \times U(1)_X$ group is broken down to $SU(2)_L\times U(1)_Y$ and a lower scale similar to the standard model one. Within the considerations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. However, the first transition in this model can be strongly first-order, which might happen at a temperature not too high above the second one. We determine the respective critical temperatures for symmetry restoration for the model.