Modular $S_3$ invariant flavor model in SU(5) GUT

Abstract: We present a flavor model with the $S_3$ modular invariance in the framework of SU(5) GUT. The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $\tau$. The GUT relation of down-type quarks and charged leptons is imposed by the VEV of adjoint 24-dimensional Higgs multiplet in addition to the VEVs of $5$ and $\bar 5$ Higgs multiples of SU(5). The observed CKM and PMNS mixing parameters as well as the mass eigenvalues are reproduced properly. We discuss the leptonic CP phase and the effective mass of the neutrinoless double beta decay with the sum of neutrino masses.