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 23 = 45° ± 0.5° and leptonic CP violating phase δ l = 260° ± 5°. The reactor angle prediction is θ 13 = 9° ± 0.5°, while the solar angle is 34° ≳ θ 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.
Highlights
The problem of understanding the quark and lepton masses, mixing angles and CP violating phases remains one of the most fascinating puzzles in particle physics
We propose an elegant theory of flavour based on A4 × Z5 family symmetry with Pati-Salam unification which provides an excellent description of quark and lepton masses, mixing and CP violation
The A4 family symmetry determines the structure of Yukawa matrices via the CSD4 vacuum alignment [33, 34], with the three columns of Y u = Y ν being proportional to (0, 1, 1)T, (1, 4, 2)T and (0, 0, 1)T, respectively, where each column has an overall phase determined by Z5 breaking, which controls CP violation in both the quark and lepton sectors
Summary
The problem of understanding the quark and lepton masses, mixing angles and CP violating phases remains one of the most fascinating puzzles in particle physics. From the point of view of extending to the quark sector, CSD4 seems to be the most promising since in unified models with Y u = Y ν, the second column is proportional to (1, 4, 2)T This simultaneously provides a prediction for both lepton mixing and the Cabibbo angle θC ≈ 1/4 in the diagonal Y d ∼ Y e basis [35]. The A4 family symmetry determines the structure of Yukawa matrices via the CSD4 vacuum alignment [33, 34], with the three columns of Y u = Y ν being proportional to (0, 1, 1)T , (1, 4, 2)T and (0, 0, 1)T , respectively, where each column has an overall phase determined by Z5 breaking, which controls CP violation in both the quark and lepton sectors. A4 group theory is discussed in appendix A and the origin of the light Higgs doublets Hu and Hd in appendix B
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