A to Z of Flavour with Pati-Salam

Abstract

Abstract:We propose an elegant theory of flavour based on A 4 × Z 5 family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation. The A 4 symmetry unifies the left-handed families and its vacuum alignment determines the columns of Yukawa matrices. The Z 5 symmetry distinguishes the right-handed families and its breaking controls CP violation in both the quark and lepton sectors. The Pati-Salam symmetry relates the quark and lepton Yukawa matrices, with Y u = Y ν and Y d ∼ Y e . Using the see-saw mechanism with very hierarchical right-handed neutrinos and CSD4 vacuum alignment, the model predicts the entire PMNS mixing matrix and gives a Cabibbo angle θ C ≈ 1/4. In particular, for a discrete choice of Z 5 phases, it predicts maximal atmospheric mixing, θ l 23 = 45 • ± 0.5 • and leptonic CP violating phase δ l = 260 • ± 5 • . The reactor angle prediction is θ l 13 = 9 • ± 0.5 • , while the solar angle is 34 • θ l 12 31 • , for a lightest neutrino mass in the range 0 m 1 0.5 meV, corresponding to a normal neutrino mass hierarchy and a very small rate for neutrinoless double beta decay.

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)…”

Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons

“…In the "indirect approach" the neutrino mass matrix is constructed from "vacuum alignments" which are orthogonal to the symmetry preserving ones, allowing the Klein symmetry to arise as an indirect consequence of the family symmetry (for a recent example of this approach see e.g. [15]). …”

“…The remnant generalized CP symmetry should be compatible with the residual Z 2 symmetry in the neutrino sector, and therefore the corresponding consistency equation should be satisfied, i.e., 15) which means that the residual CP and residual flavor transformations are commutable with each other [28,29] in the neutrino sector. For a given solution X νr of eq.…”

Supersymmetric Majoron inflation

“…the framework will be supergravity with non-minimal Kähler potential, leading to small tensor modes. It is also interesting to note that in our model the Majoron JHEP03(2017)174 field Φ may also carry flavour symmetry quantum numbers and may be considered also to be a flavon, as for example in the model in [29], where different right-handed neutrinos carry different Z N charges. Flavon inflation has for example been considered in [30][31][32].…”