Modular Symmetry with Weighton

TL;DR

This paper introduces the weighton mechanism within modular symmetry frameworks to explain fermion mass hierarchies, demonstrating how a singlet field and small parameters can reproduce observed fermion masses and mixings.

Contribution

It develops a systematic approach using weighton fields in modular symmetry models to account for fermion mass hierarchies and mixing angles, with detailed analysis for levels 3, 4, and 5.

Findings

Weighton mechanism effectively suppresses fermion masses.

Models can reproduce fermion mass and mixing hierarchies.

Examples near the CP boundary of $ au$ demonstrate viability.

Abstract

We systematically develop the weighton mechanism for natural quark and charged lepton mass hierarchies in the framework of modular symmetry with a single modulus field $\tau$. The weighton $\phi$ is defined as a complete singlet with unit modular weight, leading to fermion mass suppression by powers of $\tilde{\phi}$, which is the vacuum expectation value of the field scaled by a flavour cut-off. Further mass and mixing angle suppression comes from powers of the small parameter, $q\equiv e^{i2\pi \tau}$. Assuming some fields transform as triplets under the finite modular symmetry, with general assignments for the other fields, we perform a complete analysis for the levels $N=3, 4, 5$, expressing fermion masses and mixings in terms of powers of the small parameters $\tilde{\phi}$ and $q$. We present two examples in detail, based on the modular group $T'$, close to the CP boundary of $\tau$, which can address both fermion mass and mixing hierarchies using a weighton field.