Leptogenesis from Right-Handed Neutrino Decay in E8 ⊃ E6 × SU(3) F Unification

We compute the baryon asymmetry of the universe via thermal leptogenesis in the framework of E8 ⊃ E6 × SU(3)F unification. The right-handed neutrinos, identified as the (1,1)_1 component of the E6 27, acquire hierarchical Majorana masses from the SU(3)F breaking field Φ. The Dirac Yukawa matrix inherits the same hierarchical pattern determined in Paper II and used in Paper VIII for neutrino oscillations. Using the parameter space allowed by neutrino oscillation data (Paper VIII), we perform a comprehensive scan over the O(1) coefficients and CP phases. For each point we compute the CP asymmetry parameter ε_1 from the decay of the lightest right-handed neutrino and solve the Boltzmann equations (using the ULYSSES package) to obtain the final baryon asymmetry Y_B. We find that a large fraction of the parameter space yields Y_B within the observed range Y_B = (8.7±0.4)×10^{-11}, while simultaneously satisfying the neutrino oscillation constraints. The model predicts a normal hierarchy for the light neutrinos, with the lightest right-handed neutrino mass typically in the range 10^{15}–10^{16} GeV, and CP phases that correlate with the leptonic Dirac phase δ_CP favored near -90°. Successful leptogenesis also implies lower bounds on the reheating temperature T_RH ≳ 10^{15} GeV, consistent with GUT-scale physics and the inflation model of Paper X. This work unifies the origin of neutrino masses and the baryon asymmetry within the same E8 framework, providing a consistent picture of the early universe.