A predictive 3-3-1 model with A 4 flavor symmetry

Abstract

We propose a predictive model based on the S U(3) C ⊗S U(3) L ⊗U(1) X gauge group supplemented by the A 4 ⊗Z 3 ⊗Z 4 ⊗Z 6 ⊗Z 16 discrete group, which successfully describes the SM fermion mass and mixing pattern. The small active neutrino masses are generated via inverse seesaw mechanism with three very light Majorana neutrinos. The observed charged fermion mass hierarchy and quark mixing pattern are originated from the breaking of the Z 4 ⊗ Z 6 ⊗ Z 16 discrete group at very high scale. The obtained values for the physical observables for both quark and lepton sectors are in excellent agreement with the experimental data. The model predicts a vanishing leptonic Dirac CP violating phase as well as an effective Majorana neutrino mass parameter of neutrinoless double beta decay, with values m ββ = 2 and 48 meV for the normal and the inverted neutrino mass hierarchies, respectively.Keywords: Fermion masses and mixings, Discrete flavor symmetries, 3-3-1 models, Models beyond the Standard Model.

A 3-3-1 model with right-handed neutrinos based on the $$\varDelta \left( 27\right) $$ Δ 27 family symmetry

“…On the other hand, the existence of three fermion families, which is not explained in the context of the SM, can be understood in the framework of models with SU (3) C ⊗ SU (3) L ⊗ U (1) X gauge symmetry, called 3-3-1 models for short, where U (1) X is a nonuniversal family symmetry that distinguishes the third fermion family from the first and second ones [25,59,60,72,73,103,105,. These models have several interesting features.…”

A 3-3-1 model with low scale seesaw mechanisms

“…We use the double tetrahedral group T since it is the smallest discrete subgroup of SU (2) as well as the smallest group of any kind with 1-, 2-and 3-dimensional representations and the multiplication rule 2 ⊗ 2 = 3 ⊕ 1, thus allowing to reproduce the successful U (2) textures [64]. Note that the discrete group T [49,[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82], together with the groups A 4 [37,45,, S 4 [16,[118][119][120][121][122][123][124][125][126][127][128][129][130][131] and ∆ (27) [48,, is the smallest group containing an irreducible triplet representation that can accommodate the three fermion families of the Standard model (SM). These groups have attracted a lot of attention of the model building community since they successfully describe the observed SM fermion mass spectrum and mixing parameters.…”

Fermion masses and mixings in the 3-3-1 model with right-handed neutrinos based on the $$S_3$$ S 3 flavor symmetry

“…Models with spontaneously broken flavor symmetries may also produce hierarchical mass structures. Recently, discrete groups such as A 4 [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62], S 3 , S 4 [84][85][86][87][88][89][90][91][92][93][94], D 4 [95][96][97][98][99][100][101][102][103][104], Q 6 [105][106][107][108], T 7 [109][110][111][112][113][114]…”

“…The origin of the family structure of the fermions can be addressed in family dependent models where a symmetry distinguish fermions of different families. One explanation to this issue can be provided by the models based on the gauge symmetry SU (3) c ⊗ SU (3) L ⊗ U (1) X , also called 3-3-1 models, which introduce a family non-universal U (1) X symmetry [26,61,62,78,79,115,117,. These models have a number of phenomenological advantages.…”