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

J Sá Borges,Rudnei O Ramos

doi:10.1140/epjc/s10052-016-4168-8

J Sá Borges, Rudnei O Ramos

Open Access

https://doi.org/10.1140/epjc/s10052-016-4168-8

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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.

Highlights

On the theoretical side, some extensions of the standard model (SM) have been analyzed and the kind of scalar was selected so as to remedy the SM shortcomings
In this work we have studied the symmetry breaking patterns of the 3-3-1 model at finite temperature
Making use of the minimal version of the model, we have first analyzed its scalar sector, which is constructed from three scalars in the triplet representation of SU (3)L and the most general renormalizable interactions that can be constructed with these fields

Summary

Introduction

Some extensions of the SM have been analyzed and the kind of scalar was selected so as to remedy the SM shortcomings. Considering that the QCD asymptotic freedom condition is valid only if the number of families of quarks is less than five, one concludes that there are three generations Another interesting feature of the minimal version of the model is the prediction of an upper bound for the Weinberg angle, which follows from a peculiar relation between new gauge boson masses. We study the temperature-dependent oneloop corrected potential as a function of each value expectation value of the background fields and we graphically identify the temperature corresponding to symmetry restoration From this analysis of the temperature dependence of the oneloop corrected model spectrum, we conclude that, in the 3-31 model, it shows two scales for first-order phase transition, with the final one corresponding to the usual electroweak phase transition, as being very weak first-order, or probably second-order in practice.

The minimal version of the 3-3-1 model

Q vχ m2Q vχ0 vχ20

Mass spectrum for the scalars

The one-loop effective potential for the 3-3-1 model

Phase transition pattern in the 3-3-1 model

Conclusions