The 3-3-1 model with S 4 flavor symmetry

Abstract

We construct a 3-3-1 model based on family symmetry S 4 responsible for the neutrino and quark masses. The tribimaximal neutrino mixing and the diagonal quark mixing have been obtained. The new lepton charge L related to the ordinary lepton charge L and a SU (3) charge by L = 2 √ 3 T 8 + L and the lepton parity P l = (−) L known as a residual symmetry of L have been introduced which provide insights in this kind of model. The expected vacuum alignments resulting in potential minimization can origin from appropriate violation terms of S 4 and L. The smallness of seesaw contributions can be explained from the existence of such terms too. If P l is not broken by the vacuum values of the scalar fields, there is no mixing between the exotic and the ordinary quarks at the tree level.

A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern

“…However, the observed pattern of fermion masses and mixings was not addressed at that time due to the unexplained huge hierarchy among the Yukawa couplings [122,129,134]. Here we propose the first renormalizable extension of the 3-3-1 model with the parameter…”

“…To provide an explanation for the observed pattern of SM fermion masses and mixings, various 3-3-1 models with flavor symmetries [33][34][35][36][37][38][39][40][41][42][43][44][45][120][121][122][123] and radiative seesaw mechanisms [80,120,[124][125][126][127][128][129][130][131][132][133] have been proposed in the literature. However, some of them involve non renormalizable interactions [39,40,42,43,45], others are renormalizable but do not address the observed pattern of fermion masses and mixings due to the unexplained huge hierarchy among the Yukawa couplings [33, 35-38, 122, 123, 134] and others are only focused either in the quark mass hierarchy [34,128,130], or in the study of the neutrino sector [120, 124-127, 129, 132, 133, 135, 136], or only include the description of SM fermion mass hierarchy, without addressing the mixings in the fermion sector [131].…”

The T 7 flavor symmetry in 3-3-1 model with neutral leptons

“…This has stimulated work on flavor symmetries and non-Abelian discrete symmetries are considered to be the most attractive candidate to formulate dynamical principles that can lead to the flavor mixing patterns for quarks and lepton. There are many recent models based on the nonAbelian discrete symmetries, such as A 4 [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]34], A 5 [35][36][37][38][39][40][41][42][43][44][45][46][47], S 3 , S 4 , D 4 [117][118][119][120][121][122][123][124][125][126][127][128], D 5 [129,130], T ′ [131][132]...…”

“…In the second version, the third components of lepton triplets are the right-handed neutrinos, (ν L , l L , ν c R ) [152][153][154][155][156][157]. To have a model with the realistic neutrino mixing matrix, we should consider another variant of the form (ν L , l L , N c R ) where N R are three new fermion singlets under standard model symmetry with vanishing lepton-numbers [164][165][166][167].…”

“…In our previous works [164][165][166][167] , the discrete symmetries have been explored to the 3-3-1 models. In ref.…”