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)