Quasi two-zero texture in Type-II seesaw at fixed points from modular $A_4$ symmetry

TL;DR

The paper develops a predictive quasi two-zero neutrino mass framework within a type-II seesaw model augmented by modular $A_4$ flavor symmetry, aiming to reconcile neutrino observables with cosmological bounds on the total neutrino mass. It exploits three fixed points of the modulus $\tau$ ($i$, $\omega$, $i\infty$) to generate characteristic charged-lepton and neutrino mass textures, deriving a two-zero structure in the neutrino mass matrix $m_\nu$ via weight-10 modular forms and computing the resulting mass splittings, CP phases, and $\langle m_{ee}\rangle$ with corrections $\epsilon_{ij}$. The analysis shows that exact two-zero textures overpredict the sum of neutrino masses, necessitating controlled deviations at the fixed points to satisfy the bounds from Planck and DESI, while making concrete predictions for the neutrino sector. Overall, the work links modular flavor symmetry with cosmological constraints to produce a testable, predictive framework for neutrino masses and neutrinoless double beta decay in the near future.

Abstract

We study a quasi two-zero neutrino texture based on a type-II seesaw model with modular $A_4$ symmetry to evade the cosmological bound on the sum of neutrino masses while keeping some predictability in the neutrino sector. Working on three fixed points for modulus, we discuss predictions of the model and show the allowed points satisfying the cosmological bound on neutrino mass from both CMB and CMB+BAO data.