Multiple realizations of modular flavor symmetries and their phenomenology

TL;DR

This paper demonstrates that choosing a finite modular group like T' does not uniquely determine a modular flavor symmetry, leading to different models with distinct phenomenological implications based on their specific implementations.

Contribution

It reveals that multiple realizations of the same finite modular group can produce different modular forms and phenomenological outcomes, highlighting the importance of implementation details.

Findings

Different T' implementations yield distinct modular forms.

Model phenomenology depends on the specific realization of T'.

Multiple realizations can explain observed hierarchies differently.

Abstract

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group $T'$. Otherwise equivalent models based on different $T'$ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the $T'$ is implemented.