Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points

TL;DR

This paper develops minimal, modular flavor symmetry models for leptons near fixed points, using nonholomorphic modular forms and residual symmetries, favoring inverted neutrino mass ordering.

Contribution

It introduces highly economical lepton sector models with $S_3$ modular symmetry near fixed points, avoiding flavons and utilizing nonholomorphic modular forms.

Findings

Models favor inverted neutrino mass ordering

Constructed without flavon fields using residual symmetries

Utilized nonholomorphic modular forms as $S_3$ representations

Abstract

An extension of the Standard Model with $\Gamma_2\simeq S_3$ modular flavor symmetry is presented. We consider the construction of the lepton sector, augmented by two right-handed neutrino states, in the vicinity of the fixed points $\tau = i\infty $, $\tau = i$ and $\tau \!=\!\omega \!=\!-\frac{1}{2}\!+\!i\frac{\sqrt{3}}{2}$. Due to the residual symmetries at these points, and with the aid of nonholomorphic modular forms (which constitute representations of $S_3$) and by assigning specific transformation properties to the fermion fields, highly economical models (without flavon fields) are constructed with interesting Yukawa textures. All presented models strongly prefer the inverted ordering for the neutrino masses.