Modular Flavour Symmetries and Modulus Stabilisation

TL;DR

This paper explores how modular symmetry can be used to stabilize moduli in particle physics models, leading to spontaneous CP violation and potential explanations for fermion mass hierarchies.

Contribution

It introduces simple CP-invariant potentials within the modular symmetry framework that naturally produce CP-breaking minima near specific residual symmetry points.

Findings

CP-breaking minima occur near $ au eq i$ points

Spontaneous CP violation can explain fermion mass hierarchies

Potentially applicable to quark and lepton mass models

Abstract

We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the modulus $\tau$ we find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of $\mathbb{Z}_3^{ST}$ residual symmetry, $\tau \simeq e^{2\pi i/3}$. Stabilising the modulus at these novel minima breaks spontaneously the CP symmetry and can naturally explain the mass hierarchies of charged leptons and possibly of quarks.