Fermion hierarchies in SU(5) grand unification from Γ 6 ′ $$ {\Gamma}_6^{\prime } $$ 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 Γ 6 ′ $$ {\Gamma}_6^{\prime } $$ 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 Γ 6 ′ $$ {\Gamma}_6^{\left({}^{\prime}\right)} $$ 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.

Keywords

• Theories of Flavour
• Grand Unification