We analyse the possibility of describing quark masses, mixing and CP violation in S4′ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual Z3ST 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.
@article{arxiv.2307.14410,
title = {Quarks at the modular $S_4$ cusp},
author = {I. de Medeiros Varzielas and M. Levy and J. T. Penedo and S. T. Petcov},
journal= {arXiv preprint arXiv:2307.14410},
year = {2023}
}