Quarks at the modular $S_4$ cusp

TL;DR

This paper explores how $S'_4$ modular flavor models can explain quark masses and CP violation without flavons, emphasizing the significance of the cusp point and modular form normalization, and finds that explicit CP breaking is necessary unless a second modulus is used.

Contribution

It introduces a flavon-free $S'_4$ modular model for quark flavor physics, highlighting the role of the cusp point and modular form normalization in generating hierarchies.

Findings

Explicit CP breaking is required to fit quark data.

The cusp point influences quark mass hierarchies.

A second modulus can eliminate the need for explicit CP breaking.

Abstract

We analyse the possibility of describing quark masses, mixing and CP violation in $S'_4$ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $\mathbb{Z}^{ST}_3$ symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.