Quark masses and mixing from Modular $S'_4$ with Canonical K\"ahler Effects

TL;DR

This paper introduces a quark flavor model using modular $S'_4$ symmetry and canonical K"ahler effects, successfully fitting quark mass hierarchies and CP violation with minimal assumptions.

Contribution

It presents a novel quark flavor model based on modular symmetry and K"ahler normalization that accurately reproduces observed quark data.

Findings

Achieves a good fit to PDG 2024 quark data extrapolated to GUT scale.

Demonstrates the importance of canonical normalization in reproducing hierarchies.

Shows CP violation arises solely from the modulus $ au$.

Abstract

We propose a quark flavor model based on modular $S'_4$ with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus $\langle \tau \rangle$. We show that the canonical normalization induced by the K\"ahler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order $\mathcal{O}(1)$. 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.