A model of quark and lepton mixing

Abstract

We propose a model of quark and lepton mixing based on the tetrahedral A 4 family symmetry with quark-lepton unification via the tetra-colour Pati-Salam gauge group SU(4) P S , together with SU(2) L × U(1) R . The "tetra-model" solves many of the flavour puzzles and remarkably gives ten predictions at leading order, including all six PMNS parameters. The Cabibbo angle is approximately given by θ C ≈ 1/4, due to the tetravacuum alignment (1, 4, 2), providing the Cabibbo connection between quark and lepton mixing. Higher order corrections are responsible for the smaller quark mixing angles and CP violation and provide corrections to the Cabibbo and lepton mixing angles and phases. The tetra-model involves an SO(10)-like pattern of Dirac and heavy right-handed neutrino masses, with the strong up-type quark mass hierarchy cancelling in the see-saw mechanism, leading to a normal hierarchy of neutrino masses with an atmospheric angle in the first octant, θ l 23 = 40 • ± 1 • , a solar angle θ l 12 = 34 • ± 1 • , a reactor angle θ l 13 = 9.0 • ± 0.5 • , depending on the ratio of neutrino masses m 2 /m 3 , and a Dirac CP violating oscillation phase δ l = 260 • ± 5 • .

Littlest Seesaw model from S 4 × U(1)

“…(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].…”

“…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)…”

A to Z of Flavour with Pati-Salam

“…Different choices of phase for η are theoretically possible, but the phenomenologically successful choice for the relative phase of the atmospheric and solar terms (the first and second terms in eq. (5.5)) is η = 2π/5, whereas for example η = −2π/5 leaves the mixing angles unchanged but reverses the sign of the CP phases [33][34][35]. The dependence on see-saw phases was fully discussed in [33].…”

“…With a diagonal right-handed Majorana mass matrix, Y ν leads to a successful prediction of the PMNS mixing parameters [34]. Also the Cabibbo angle is given by θ C ≈ 1/4 [35]. Thus eq.…”

Towards predictive flavour models in SUSY SU(5) GUTs with doublet-triplet splitting

“…An approach to flavour (GUT) model building with diagonal Y e (and Y d ) has been discussed recently in [33,34]. We introduce flavon fields θ 1 , θ 2 , θ 3 and θ 4 that obtain a VEV and generate the hierarchical structure of the Yukawa matrices.…”