Abstract
We construct a supersymmetric model for leptons and quarks with the flavor symmetry Δ(384) and CP. The peculiar features of lepton and quark mixing are accomplished by the stepwise breaking of the flavor and CP symmetry. The correct description of lepton mixing angles requires two steps of symmetry breaking, where tri-bimaximal mixing arises after the first step. In the quark sector the Cabibbo angle θC equals sinπ/16≈0.195 after the first step of symmetry breaking and it is brought into full agreement with experimental data after the second step. The two remaining quark mixing angles are generated after the third step of symmetry breaking. All three leptonic CP phases are predicted, sinδl≈−0.936, |sinα|=|sinβ|=1/2. The amount of CP violation in the quark sector turns out to be maximal at the lowest order and is correctly accounted for, when higher order effects are included. Charged fermion masses are reproduced with the help of operators with different numbers of flavor (and CP) symmetry breaking fields. Light neutrino masses, arising from the type-I seesaw mechanism, can accommodate both mass orderings, normal and inverted. The vacuum alignment of the flavor (and CP) symmetry breaking fields is discussed at leading and at higher order.
Highlights
Crucial features of the elementary fermions, such as the hierarchy among the charged fermion masses, the pattern of lepton and quark mixing and the striking difference between these two, C
The paper is structured as follows: in section 2 we present an outline of the model, comprising the relevant symmetries of the model, the transformation properties of the minimal SUSY SM (MSSM) superfields and νc, the different steps of the flavor and CP symmetry breaking and the results for fermion masses and mixing
We find that CP violation is maximal at the lowest order in the quark sector, see Eqs. (96) and (97), and corrections are of relative order λ, see Eq (98), leading to JCqP being in full accordance with the experimental results [30]
Summary
Crucial features of the elementary fermions, such as the hierarchy among the charged fermion masses, the pattern of lepton and quark mixing and the striking difference between these two,. The Dirac phase δl fulfills sin δl ≈ −0.936, meaning δl is close to 3 π/2, as hinted at by the√experimental data [29], while for both Majorana phases α and β we find | sin α| = | sin β| = 1/ 2 These results agree with those, obtained in a model-independent analysis of mixing patterns that originate from a flavor symmetry (3 n2) or (6 n2) and CP, if the latter are broken to a residual Z3 symmetry among charged leptons and to Z2 × CP in the neutrino sector [18,19]. Appendix D contains information about a possible UV completion of the relevant operators at leading and at higher order that contribute to fermion masses and mixing
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