Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification

Abstract

We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification. The tribimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3). We construct a realistic model of quark and lepton masses and mixings based on SO (3) These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.

A model of quark and lepton mixing

“…The unification of quarks and leptons in terms of A4SU421 is depicted in figure 1. The model involves U(1) R , rather than SU(2) R , used in previous models [20], in order to allow diagonal charged lepton and down quark Yukawa matrices together with off-diagonal neutrino and up quark Yukawa matrices. Quark mixing then arises completely from the up quark Yukawa matrix, which is equal to the neutrino Yukawa up to Clebsch-Gordan coefficients.…”

“…ous forms of constrained sequential dominance (CSD) have been considered based on the atmospheric neutrino alignment (0, 1, 1) but with different forms of solar neutrino alignment: original CSD [25] involved a solar alignment (1, 1, −1) yielding tri-bimaximal (TB) mixing; CSD2 [26,27] involved a solar alignment (1, 2, 0) and hence a small reactor angle; CSD3 [13] involved solar alignment (1, 3, 1) with an acceptable reactor angle but maximal atmospheric mixing; CSD4 [12] with the tetra-alignment (1, 4, 2) adopted here predicts best fit lepton angles with a normal hierarchy. By unifying leptons with quarks, we show here for the first time that CSD4 can also successfully predict the Cabibbo angle.…”

“…In the Majorana sector the Z 5 allowed leading operators are diagonal and given by, 20) where ξ j are three singlets under both A 4 and the Pati-Salam group. The operators relevant for the heavy Majorana mass matrix M R , emerging from eq.…”

Littlest Seesaw model from S 4 × U(1)

“…However sharp predictions for the reactor (and solar) angles can only result from applying constraints to the Dirac mass matrix of various types, an approach known as constrained sequential dominance (CSD) [24]. For example, keeping the first column of the Dirac mass matrix fixed (0, a, a) T , a class of CSDn models has emerged [18,[24][25][26][27][28][29] corresponding to the second column taking the form (b, nb, (n − 2)b) T , with a reactor angle approximately given by [30] θ 13 ∼ (n − 1)…”

“…where CSD1 [24] implies tri-bimaximal (TB) mixing with a zero reactor angle, CSD2 [25] has a reactor angle θ 13 ∼ √ 2 3 m 2 m 3 , which is too small, CSD3 [18] in eq. (1.1) predicts θ 13 ∼ 2 √ 2 3 m 2 m 3 which is in good agreement with the experimental value θ 13 ∼ 0.15 [1], and CSD4 [26][27][28] predicts θ 13 ∼ √ 2 m 2 m 3 , while higher values of n > 4 involve increasingly large values of the reactor angle which are disfavoured [29].…”