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

We consider the minimal version of an extension of the standard electroweak model based on the S U ( 3 ) c × S U ( 3 ) L × 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 S U ( 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 S U ( 3 ) L × U ( 1 ) X group is broken down to S U ( 2 ) L × 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.