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

Abstract

Abstract 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.