Neutrino Masses and Mixing from E 8 ⊃ E 6 × S U ( 3 ) F Unification

We present a comprehensive analysis of neutrino masses and mixing within the E8 ⊃ E6 × SU(3)F unification framework. The right-handed neutrinos are naturally identified as the (1,1)_1 component of the E6 27 representation. Their Majorana masses arise from couplings to the SU(3)F adjoint field Φ, which acquires a GUT-scale vacuum expectation value ⟨Φ⟩ ∼ M_GUT = 1.2×10^16 GeV (Paper III). Using the hierarchical Yukawa pattern derived in Paper II, we construct the Dirac mass matrix and apply the type I seesaw mechanism. By performing a systematic scan over the O(1) coefficients that parameterize the allowed flavor structure, we show that the observed neutrino mass squared differences Δm_21^2 ≈ 7.4×10^{-5} eV^2 and |Δm_31^2| ≈ 2.5×10^{-3} eV^2 are naturally reproduced with a normal mass hierarchy. The model predicts the lightest neutrino mass m_1 ∼ (1–5)×10^{-3} eV and the effective Majorana mass for neutrinoless double beta decay m_ββ ≈ 3–10 meV, within the reach of next-generation experiments (LEGEND, nEXO). The leptonic mixing angles are found to be in agreement with current global fits, with a preference for θ_23 in the upper octant and δ_CP ∼ −π/2. Lepton flavor violating processes such as μ → eγ are predicted to have branching ratios BR(μ→eγ) ∼ 10^{-13}–10^{-14}, potentially observable by MEG II and future facilities. This work extends the E8 unification program to the neutrino sector, providing testable predictions for upcoming experiments.