Neutrino mixing with nonzero θ13 and CP violation in the 3-3-1 model based on S4 flavor symmetry

Abstract

The 3-3-1 model proposed in 2011 based on discrete symmetry [Formula: see text] responsible for the neutrino and quark masses is updated, in which the nonzero [Formula: see text] is focused. Neutrino masses and mixings are consistent with the most recent data on neutrino oscillations without perturbation. The new feature is adding a new [Formula: see text] anti-sextet lying in doublet under [Formula: see text] which can result the nonzero [Formula: see text] without perturbation, and consequently, the number of Higgs multiplets required is less than those of other models based on non-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximal form obtained with the breaking [Formula: see text] in charged lepton sector and [Formula: see text] in neutrino sector. If both breakings [Formula: see text] and [Formula: see text] are taken place in neutrino sector, the realistic neutrino spectrum is obtained without perturbation. The upper bound on neutrino mass and the effective mass governing neutrinoless double beta decay at the tree level are presented. The model predicts the Dirac CP violation phase [Formula: see text] in the normal spectrum (with [Formula: see text]) and [Formula: see text] in the inverted spectrum.

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

“…[36][37][38][39] for recent reviews on flavor symmetries). Recently, extensions of the SM with A 4 , S 3 [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], S 4 [77][78][79][80][81][82][83][84][85][86], D 4 [87][88][89][90][91][92][93][94][95][96], T 7 [97][98][99][100][101][102][103][104][105][106], T 13 [107][108][109]…”

The Δ(27) flavor 3-3-1 model with neutral leptons

“…Models with spontaneously broken flavor symmetries may also produce hierarchical mass structures. Recently, discrete groups such as A 4 , S 3 [61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], S 4 [77][78][79][80][81][82][83][84][85], D 4 [86][87][88][89][90][91][92][93][94][95], T 7 [96][97][98][99][100][101][102][103][104][105], T 13 [106][107][108][109], T ′ [110]…”

Generating lepton masses and mixings with a heavy vector doublet

“…[1][2][3][4][5]. Several discrete groups such as S 3 , A 4 , S 4 [77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94] , D 4 [95][96][97][98][99][100][101][102][103], Q 6 [104][105][106][107][108][109][110][111][112][113][114], T 7 [115][116][117][118][119][120][121][122][123]…”