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

A bstract We construct an SU (5) grand unified model in which the hierarchies of the quark and lepton masses and mixing are explained by the ₆^ Γ 6 ′ modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual Z₆T Z 6 T symmetry, approximately unbroken at τ ~ i∞. We argue that the ₆^ ({^) } 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.