Neutrino mass predictions with metaheuristic optimization under $$A_4$$ modular symmetry

The current research aims to conduct an exhaustive investigation of the neutrino mass model based on \(A_4\) discrete non-abelian modular symmetry, specifically in the context of the linear seesaw mechanism, where the conventional type I seesaw mechanism is extended, with particular attention given to the optimization of the parameters using incomprehensible but intelligible-in-time logics optimization algorithm (ILA), a metaheuristic optimization. Unlike other approaches to discrete flavor symmetry, the modular approach to flavor dynamics is found to significantly reduce the number and complexity of flavon fields required to give realistic textures to fermion masses. The key predictions include neutrino masses, \(U_\text {PMNS}\) matrices, effective neutrino masses for neutrinoless double beta decay, beta decay, Dirac and Majorana CP violation phases for normal (NO) and inverted mass ordering (IO), offering testable implications. The working efficiency of the ILA optimization technique is also estimated. The optimized neutrino oscillation parameters are well consistent with recent experimental data. Our analysis also aligns with Planck cosmological constraints on the sum of neutrino masses \(0.06<\Sigma m<0.12\ \text {eV}\) .