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

The European Physical Journal C, Jun 2016

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.

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

Eur. Phys. J. C Symmetry breaking patterns of the 3-3-1 model at finite temperature J. Sá Borges 1 Rudnei O. Ramos 0 0 Departamento de Física Teórica , Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ 20550-013 , Brazil 1 Departamento de Física de Altas Energias , Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ 20550-013 , Brazil We consider the minimal version of an extension of the standard electroweak model based on the SU (3)c × SU (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 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 × U (1)X group is broken down to SU (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. 1 Introduction Extensive work has been dedicated to the study of the electroweak phase transition in the standard model (SM) as well as in many of its extensions. This interest is based for a large part on the possibility that it might explain the baryon asymmetry in the universe and that this asymmetry could be produced at around the scale of the electroweak symmetry breaking in the primordial hot Big Bang universe (for reviews see, e.g., Refs. [1–3]). One of the necessary conditions for a model to explain the baryon asymmetry of the universe is the presence of nonequilibrium effects. In a phase transition, this can be achieved if the transition is first-order and its strength is strong enough, in what is usually called a strong first-order phase transition. This condition is parameterized by the ratio R = φ (Tc)/ Tc, where φ (Tc) is the value for the degenerate vacuum for the Higgs field at the critical temperature Tc. A strong first-order phase transition is usually characterized by the condition R > 1. In the SM this condition cannot be achieved. Lattice Monte Carlo numerical simulations of the electroweak standard model [4–6] have shown that there is an endpoint in the phase diagram of the model for a Higgs mass mH ∼ 80 GeV, where the phase transition is weak first-order as the endpoint is approached from the left and the transition becomes a smooth crossover for larger Higgs masses. According to recent results from the Large Hadron Collider (LHC), from the current combined results from ATLAS and CMS experiments [7] have indicated the existence of a Higgs boson with a mass 125.1 ± 0.3 GeV. Thus, this gives no hope of achieving the necessary conditions for producing a baryon asymmetry in the context of the SM, since no significant departure from thermal equilibrium can be obtained during the phase transition dynamics. This is one of the motivations for looking for extensions of the SM and/or alternative models and the searches for new scalar particles at the LHC, aiming to reveal the ingredients needed for the strong first-order electroweak phase transition (EWPT), as required to produce the resulting observed baryon asymmetry. On the theoretical side, some extensions of the SM have been analyzed and the kind of scalar was selected so as to remedy the SM shortcomings. These extensions used to enhance the SM are usually constructed with a scalar gauge singlet [8], a complex scalar or a scalar from supersymmetric degrees of freedom (in the context of supersymmetry extensions of the SM) [9]. On the other hand, there are alternative models, with a larger particle spectrum than the SM, that predict the existence of new gauge bosons and exotic quarks that acquire mass from their couplings to new scalar fields. In particular, in this paper, we are exploring the phenomenological aspects of an alternative to the SM based on the SU ( 3 )c × SU ( 3 )L × U ( 1 )X gauge symmetry, commonly known as the 3-3-1 model [10,11]. In this model, the scalars are accommodated in a convenient fundamental representation of the SU ( 3 )L symmetry group. From the electric charge operator one can select its model version. One particular version predicts the existence of new very massive gauge bosons and exotic quarks. In this work, we want to study and better understand the possible phase transition sequences associated with the symmetry breaking pattern SU ( 3 )L ⊗ U ( 1 )X → SU ( 2 )L ⊗ U ( 1 )Y → U ( 1 )E M (...truncated)


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J. Sá Borges, Rudnei O. Ramos. Symmetry breaking patterns of the 3-3-1 model at finite temperature, The European Physical Journal C, 2016, pp. 344, Volume 76, Issue 6, DOI: 10.1140/epjc/s10052-016-4168-8