Abstract
We propose an extension of the 3-3-1 model with an additional symmetry group {Z}_2times {Z}_4times mathrm{U}{(1)}_{L_g} and an extended scalar sector. To our best knowledge this is the first example of a renormalizable 3-3-1 model, which allows explanation the SM fermion mass hierarchy by a sequential loop suppression: tree-level top and exotic fermion masses, 1-loop bottom, charm, tau and muon masses; 2-loop masses for the light up, down, strange quarks as well as for the electron. The light active neutrino masses are generated from a combination of linear and inverse seesaw mechanisms at two loop level. The model also has viable fermionic and scalar dark matter candidates.
Highlights
The model reproduces fairly well the hierarchical structure of the observable quark mass spectrum as a result of the sequential loop suppression mechanism, where the top quark mass is generated at tree level, the masses for the bottom and charm quarks arise at one loop level and the light up, down and strange quarks get their masses at two loop level
The light active neutrinos acquire their masses from a combination of linear and inverse seesaw mechanisms at two loop level
At tree level there is no quark mixing, the mixing angles in the quark sector are generated from a combination of one and two loop level radiative seesaw mechanisms
Summary
Majorana neutrinos in the SU(3)L lepton triplet was proposed for the first time in [138]. Despite the fact that the scalar and fermion sectors of our model are considerably larger than the corresponding to the simplified version of the [3-1] model with β = − √1 , and the fields assignments under the discrete group Z4 × Z2 look rather sophisticated, each introduced element plays its own role in the implementation of the radiative seesaw mechanisms that allow us to explain the SM fermion mass hierarchy by a sequential loop suppression. The Z4 charged SU(3)L scalar singlet φ01 is needed for the implementation of the one loop level radiative seesaw mechanism that generates the charm, the bottom quark masses as well as the tau and muon lepton masses, as shown in figure 2. The SU(3)L scalar singlet ξ0 is introduced to spontaneously break the U(1)Lg generalized lepton number symmetry and giving rise to a tree-level mass for the right handed Majorana neutrino ΨR.
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