Introduction
The confirmation of the Higgs boson with a mass of 126 GeV in July 2012 has marked a milestone in Particle Physics, consolidating the standar model (SM) of elementary particles as one of the most successful models of Theoretical Physics [1-3]. The SM is based on the symmetry group SU(3)C ⊗ SU(2)L ⊗ U (1)Y, which identifies elementary particles and explains their interactions. There is currently no experimental data that can decisively contradict their predictions; however, the description provided by the SM is incomplete, since there are experimental observations that it can not explain, such as: the violation of leptonic universality, the proliferation of fermionic generations and their mass spectrum, the CP violation mechanisms, symmetry breaking, the large number of arbitrary parameters and neutrino oscillation. Likewise, it does not include gravity and leaves out the explanation of dark matter and energy. For these reasons, it is important to study extensions of the SM such as Technicolor [4], Supersymmetric Models, or 3-3-1 Model and their different mechanisms to try to respond to the aforementioned problems.
Currently, research at TeV energy scales is of great importance for Particle Physics, because it can clarify many of the above-mentioned questions. In this sense, the 3-3-1 Model with heavy leptons [5], whose symmetry group is SU(3)C ⊗ SU(3)L ⊗ U(1)N, is a good alternative, where the subgroup SU(3)L ⊗ U(1)N of the electroweak interactions is an extension of the symmetry group SU(2)L ⊗ U(1)y of SM.
The 3-3-1 Model adds heavy charged leptons to the doublets of the SM, extending it to triplets [6] and in the Higgs sector it considers three scalar triplets, unlike the SM, which has only one doublet. The new particles generated in this model acquire mass through spontaneous symmetry breaking, being the Higgs sector the most extended, with: neutral Higgs (
In this present work a brief overview of the 3-3-1 Model with heavy leptons is presented, the total decay width of the charged Higgs boson
Additionally, to verify the existence of the particles postulated by 3-3-1 Model, either in high energy hadronic accelerators such as the Large Hadron Collider(LHC), which is expected to reach energies of up to 28 and 100 TeV, and which could be able to obtain signals from Higgs sector and non-standard gauge particles, or in linear colliders of the e
+
e
- type such as the Compact Linear Collider (CLIC), which has its simpler initial states and leads to easier final states to identify. For example, when the production of heavy leptons (e+e-
→
c
Particles of 3-3-1 Model
Quarks Sector
In 3-3-1 Model, quarks and leptons are treated in a different way. In the quark sector we have the following left-hand particles:
where the first family of quarks belongs to the fundamental representation of SU(3)l, while the second and third belong to the adjoint representation. The particles J i and J α (α = 2, 3) are exotic quarks and have a charge of (5e/3) and (-4e/3), respectively [7,8]. Right-handed quarks
with U = u; c; t and D = d; s; b, are transformed as singlets under the SU(3)L group.
Leptons Sector
The leptonic sector is made up of the following left-hand particles:
where l = e; μ; т and P l = E; M; T.
Unlike quarks, in leptons all families belong to the same representation of the SU(3)l group. This sector also presents its right-handed counterpart:
Like quarks, right-handed leptons also transform as singlets under the SU(3) L . The values 0, 2/3 and -1/3 presented in the description of quarks and leptons represent the charge of the group U(1) N [5].
Higgs Sector
It is the most abundant sector, apart from containing the Higgs
The minimal scalar sector of 3-3-1 Model contains the following triplets, η, p and χ [5,7]:
whose expected vacuum values of its neutral components are:
and satisfy:
where υW is the expectation value of vacuum (VEV) or Weinberg value of vacuum. The pattern of the symmetry breaking is given by [6]:
After breaking of symmetry, the masses of scalar fields are given by:
where f is a constant with dimension of mass and the λi (i = 1, 2..., 10) are dimensionless constants. In addition, it is considered that υ χ ≫ υ p,η and the condition is imposed by f ≈ - υχ [6].
Gauge Sector
In addition to the intermediate particles of SM (γ, W± and Z), the 3-3-1 Model predicts the existence of the neutral boson Z', two singly charged bosons V ± and two doubly charged bosons U ±±. The interaction between gauge and Higgs bosons results from the lagrangian:
where the covariant derivative is given by:
where Nφ are the charges of the group U(1)
N
for the triplets (p = η,p,χ),
The masses of the new bosons as a function of the Weinberg angle θ W , of the expected values of the vacuum and the elemental charge e of the electron, are:
where:
Decay of Higgs
The production of charged Higgs
The
The total width of decay of the Higgs
where Γ
XY
= r(
The contribution of each term is given by:
The V-(V
+) decays in
The total width of decay of boson V ± is given by:
where Γ XY = Γ(V± → XY).
The contribution of each term is given by:
Where
Results and Conclusions
In this work we present the widths of the
f | v χ , mJ 1 | m E | m M |
|
|
|
m V | m u | M Z' |
---|---|---|---|---|---|---|---|---|---|
-4000 | 4000 | 595.60 | 3500.02 | 1264.91 | 5756.99 | 4068 75 | 1837.72 | 1836.83 | 6830.21 |
-5000 | 5000 | 744.50 | 4375.00 | 1581.46 | 7198.47 | 5086.95 | 2296.63 | 2295.91 | 8539.47 |
Unlike other papers [7,8,10], in which arbitrary parameters were taken, in this work the representative values given above are considered for these parameters and the VEV's. This model, in particular, includes heavy leptons and also the condition -f ≃vx, different from other models, because of which the phenomenology must be different. Consequently, it should be noted that the decay widths of
Since the Higgs
Decay of the
From Figures 1a and 1b it can be seen that, for vx = 4.0(5.0) TeV, depending on the effective cross section, the channel
These final two leptons E
-
,ve are relatively easy to register on the detector, as charged heavy lepton leaves a trace. To record them, the invariant mass of the pair will be calculated, where the charged Higgs boson will be observed in the invariant mass distribution. With respect to
From the same figures it is observed that for masses greater than or equal to 1930.00(2392.00) GeV for the
Other less promising channels, which may give some contribution to the signal, depending on the effective cross section and the luminosity of the machine, would be: