Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points

TL;DR

This work demonstrates that a minimal modular flavor framework based on Gamma2-S3, with a single modulus tau and no flavons, can naturally address lepton masses and neutrino oscillations. By exploiting non-holomorphic modular forms and residual symmetries at fixed points tau near i_infinity and tau near i, the authors construct economical lepton textures with two right-handed neutrinos and a type-I seesaw, achieving inverted ordering as a robust outcome. Concrete IO fits are obtained, including realistic light-neutrino masses, mixing angles, CP phases, and small m_beta_beta, while heavy RHN scales lie around 10^14 GeV. The results suggest that fixed-point modular symmetry can yield predictive lepton textures with a very limited scalar sector, motivating exploration of larger modular groups and the quark sector.

Abstract

An extension of the Standard Model with $Γ_2\simeq S_3$ 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 $τ= i\infty $ and $τ= i$. Due to the residual symmetries at these points, and with the aid of non-holomorphic 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.

Figures (1)

• Figure 1: Values of $\delta$ and $\rho_1$ (green shade) for IO neutrinos, giving $|\frac{\epsilon_0}{\sqrt{n}}|\leq 0.2$ [see e.g. Eq. (\ref{['orig-pars']})]. Used the bfvs of the oscillation parameters Capozzi:2021fjo.