Abstract
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.
Highlights
The atmospheric mixing angle θ2l 3 49.2◦ are large, and the reactor mixing angle is small with θ1l 3 8.57◦, while the CP violation of the lepton sector has not been confirmed yet [4]
The modular form of level N and integral weight k can be arranged into some modular multiplets of the homogeneous finite modular group ΓN ≡ Γ/Γ(N ) [7], and they can be organized into modular multiplets of the inhomogeneous finite modular group ΓN ≡ Γ/Γ(N ) if k is an even number [6]
The role of modular invariance as flavor symmetry can overcome the drawback of the conventional discrete flavor symmetry models
Summary
We formulate our models in the framework of supersymmetric SU(5) GUT. The neutrino masses are generated by the type-I seesaw mechanism [66,67,68,69,70], three (or two) right-handed neutrinos N are introduced and they are SU(5) singlets. All the three Higgs fields are assumed to be invariant under A4 and their modular weights are zero. Each of these GUT Higgs representations contains an SU(2)L Higgs doublet, the low energy doublet Hu in the minimal supersymmetric standard model arises from H5, and Hd originates from a linear combination of H5 and H45. The most general superpotential for quark and lepton masses is of the following form,. We shall present the most general form of the mass matrices of quarks and leptons in SU(5) models with A4 modular symmetry. We shall consider modular forms up to weight 8 in the following, and extension to higher weight modular forms is straightforward
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
