Flipped SU(5) with modular $A_4$ symmetry

We have investigated the modular binary octahedral group 2O as a flavor symmetry to explain the structure of Standard Model. The vector-valued modular forms in all irreducible representations of this group are constructed. We have classified all possible fermion mass models based on the modular binary octahedral group 2O. A comprehensive numerical analysis is performed, and we present some benchmark quark/lepton mass models in good agreement with the experimental data. Notably we find a minimal modular invariant model for leptons and quarks, which is able to explain simultaneously the masses and mixing parameters of both quarks and leptons in terms of 14 real free parameters including the modulus τ. The fermion mass hierarchies around the vicinity of the modular fixed points are explored.

Section: Jhep11(2023)083mentioning

confidence: 99%

Modular binary octahedral symmetry for flavor structure of Standard Model

Ding,

Liu,

et al. 2023

“…In fact, we can find isomorphisms Γ 2 ≃ S 3 , Γ 3 ≃ A 4 , Γ 4 ≃ S 4 , and so on. There have been many attempts to understand the flavor structures of the SM by the finite modular flavor symmetries , especially under the GUTs [84][85][86][87][88][89][90][91][92].…”

Section: Jhep08(2023)097mentioning

confidence: 99%

Fermion hierarchies in SU(5) grand unification from $$ {\Gamma}_6^{\prime } $$ modular flavor symmetry

Abe,

Higaki,

Kawamura

et al. 2023

We construct an SU(5) grand unified model in which the hierarchies of the quark and lepton masses and mixing are explained by the $$ {\Gamma}_6^{\prime } $$ Γ 6 ′ modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual $$ {Z}_6^T $$ Z 6 T symmetry, approximately unbroken at τ ~ i∞. We argue that the $$ {\Gamma}_6^{\left({}^{\prime}\right)} $$ Γ 6 ′ symmetry is the minimal possibility to realize the up-type quark mass hierarchies, since the Yukawa matrix is symmetric. We find a combination of the representations and modular weights and then show numerical values of (1) coefficients for the realistic fermion hierarchies.

“…Therefore there is a strong motivation for introducing modular symmetry in the context of GUTs such that the complication of flavor symmetry breaking can be removed and the predictive power of the GUTs models can be improved considerably. The possible combinations of SU(5) GUTs and modular symmetry groups have been discussed in the literature, and several modular SU(5) GUT models have been built at level 2 [10,66], level 3 [14,67,68] and level 4 [69][70][71].…”

Section: Jhep10(2022)071mentioning

confidence: 99%

Leptogenesis in SO(10) models with A4 modular symmetry

Ding

King

et al. 2022

Self Cite

We study the prediction for leptogenesis in two renormalizable supersymmetric SO(10) × A4 modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless double beta decay and the leptonic CP violation phases are discussed.