Double covering of the modular A 5 group and lepton flavor mixing in the minimal seesaw model

We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

Section: Introductionmentioning

confidence: 99%

Modular invariant A4 models for quarks and leptons with generalized CP symmetry

Yao

Ding

2021

“…1 Indeed, various modular invariant models which successfully reproduce the SM have been constructed in these years, e.g. for Γ 2 [14][15][16][17], Γ 3 [1,2,14,[17][18][19][20][21][22][23][24], Γ 4 [17,20,[25][26][27][28], Γ 5 [17,28,29], Γ 7 [30], and the double covering groups of the modular groups [17,[31][32][33][34][35][36][37]. A combined symmetry of the modular symmetry with the conventional flavor symmetries or CP-symmetry is also considered in [38][39][40][41][42][43][44][45].…”

Section: Jhep07(2021)068mentioning

confidence: 99%

“…Their matrix representations are summarized in table 10. The complete table of the irreducible decomposition of the tensor products, and their CG coefficients also can be found in [35]. The JHEP07(2021)068 irreducible decomposition of the tensor products of the triplets are given by…”

Section: Jhep07(2021)068mentioning

confidence: 99%

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Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism

Kuranaga

Ohki

Uemura

2021

We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in the quark sector. The FN mechanism requires an extra U(1) gauge symmetry which is broken at high energies. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra U(1) symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for the quark sector. Assuming that the three generations have a common representation under the modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related to each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.

“…All the modular forms of integral weights can be generated from the tensor products of weight one modular forms and the odd weight modular forms are in the representations with ρ r (S 2 ) = −1. The homogeneous finite modular groups Γ N provide richer structure of modular forms for flavor model building, and the small groups Γ 3 ∼ = T [7,49], Γ 4 ∼ = S 4 [50,51] and Γ 5 ∼ = A 5 [52] have been studied. If the modular weight k of the operator is not an integer, (cτ +d) k is not the automorphy factor anymore and some multiplier is needed, consequently the modular group should be extended to its metaplectic covering [53].…”

Section: Introductionmentioning

confidence: 99%

SU(5) GUTs with A4 modular symmetry

Chen

Ding

King

2021

We combine SU(5) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the representation assignments of the matter fields under A4, we find that there are seven types of SU(5) models with A4 modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models.