Fermion hierarchies in SU(5) grand unification from $$ {\Gamma}_6^{\prime } $$ modular flavor symmetry
Yoshihiko Abe (Department of Physics, University of Wisconsin, Madison, WI, 53706, USA); Tetsutaro Higaki (Department of Physics, Keio University, Yokohama, 223-8522, Japan); Junichiro Kawamura (Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34051, Korea); Tatsuo Kobayashi (Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan)
We construct an SU(5) grand unified model in which the hierarchies of the quark and lepton masses and mixing are explained by the $$ {\Gamma}_6^{\prime } $$ modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual $$ {Z}_6^T $$ symmetry, approximately unbroken at τ ~ i∞. We argue that the $$ {\Gamma}_6^{\left({}^{\prime}\right)} $$ 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.