Fermion hierarchies in SU(5) grand unification from G'(6) modular flavor symmetry

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)' modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual Zeta(T)(6) symmetry, approximately unbroken at tau similar to i infinity. We argue that the Gamma(('))(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 O(1) coefficients for the realistic fermion hierarchies.

Automated summary

We propose an SU(5) grand unified model that explains the hierarchies of quark and lepton masses and mixing using the Gamma(6)' modular flavor symmetry. The hierarchical structure is achieved through the Froggatt-Nielsen-like mechanism based on the residual Zeta(T)(6) symmetry. We demonstrate that the Gamma(('))(6) symmetry is the minimal possibility to account for the up-type quark mass hierarchies, given the symmetric nature of the Yukawa matrix. We determine the appropriate combination of representations and modular weights, and provide numeric values for the realistic fermion hierarchies.