Particle Swam Optimization Based Analysis to Unlocking the Neutrino Mass Puzzle using A₄ Z₃ Z₁₀ Flavor Symmetry

New research has highlighted a shortfall in the Standard Model (SM) because it predicts neutrinos to have zero mass. However, recent experiments on neutrino oscillation have revealed that the majority of neutrino parameters indeed indicate their significant mass. In response, scientists are increasingly incorporating discrete symmetries alongside continuous ones for better justification of observed patterns of neutrino mixing. In this study, we have examined a model within A₄ Z₃ Z₁₀ symmetry to estimate the neutrino masses using particle swam optimization technique for both mass hierarchy of neutrino. This model employed a hybrid seesaw mechanism, a combination of seesaw mechanism of type-I and type-II, to establish the effective Majorana neutrino mass matrix. After calculating the mass eigenvalues and lepton mixing matrix upto second order perturbation theory in this framework, this study seeks to investigate the scalar potential for vacuum expectation values (VEVs), optimize the parameters, U₏₌₍ₒ matrix, neutrino masses: |m₁^{}N|=0. 0292794-0. 0435082\ eV, |m₂^{}N|=1. 78893 10^-18-0. 0293509\ eV, |m₃^{}N|=0. 0307414-0. 0471467\ eV, |m₁^{}I|=0. 00982013-0. 0453623\ eV, |m₂^{}I_|=0. 0379702-0. 0471197\ eV, and |m₃^{}I|=0. 0122063-0. 027544\ eV, effective neutrino mass parameters: m₄₄ N= (0. 170-3. 93) 10^-2\ eV, m_{} N= (0. 471-1. 39) 10^-2\ eV, m₄₄ I= (1. 85-4. 55) 10^-2\ eV and m_{} I= (2. 26-4. 56) 10^-2\ eV, are predicted for both mass hierarchy through particle swam optimization (PSO), showing strong agreement with recent experimental findings.