SO(10) models with A4 modular symmetry

A bstract We combine SO(10) Grand Unified Theories (GUTs) with 4 modular symmetry and present a comprehensive analysis of the resulting quark lepton mass matrices for all simplest cases. focus on case where three fermion families in 16 dimensional spinor representation form triplet ? 3 ? , Higgs sector comprising single multiplet H 10 fundamental one field $$ \overline{\Delta } ? ¯ \overline{\mathbf{126}} 126 minimal models, plus ? 120 non-minimal specified weights. The neutrino masses are generated by type-I and/or type II seesaw mechanisms results presented each model following an intensive numerical we have optimized free parameters models order to match experimental data. For phenomenologically successful best fit tabular as well showing most interesting graphical correlations between parameters, including leptonic CP phases neutrinoless double beta decay, which yet be measured, leading definite predictions models.