Quark masses and mixing from modular $$ {S}_4^{\prime } $$ with canonical Kähler effects

A bstract We propose a quark flavor model based on modular $$ {S}_4^{\prime } $$ S 4 ′ with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus 〈 τ 〉. We show that the canonical normalization induced by the Kähler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order $$ \mathcal{O}(1) $$ O 1 . The minimal model achieves a great fit to the quark sector data, which we take as the PDG 2024 data extrapolated to the GUT scale.