Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism

TL;DR

This paper introduces a novel flavor model for quark mass hierarchies using modular symmetry, replicating Froggatt-Nielsen mechanisms without requiring extra gauge symmetries, and successfully reproduces realistic quark masses and mixings.

Contribution

It presents new quark flavor models based on modular symmetry that naturally generate mass hierarchies and mixing angles without hierarchical parameters, extending Froggatt-Nielsen ideas.

Findings

Models reproduce realistic quark mass hierarchies.

Mixing angles are related to modular parameters.

No unnatural hierarchical parameters are needed.

Abstract

We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in quark sector. The FN mechanism requires an extra $U(1)$ gauge symmetry which is broken at high energy. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra $U(1)$ symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for quark sector. Assuming that the three generations have a common representation under modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.