Thermal Leptogenesis in $SO(10)\times U(1)_A$ SUSY GUT

We investigate thermal leptogenesis within a supersymmetric grand unified theory (SUSY GUT) based on the $SO(10) \times U(1)_A$ symmetry, where both the doublet--triplet splitting problem and the unrealistic Yukawa relations are resolved under the natural assumption that all symmetry-allowed interactions appear with $\mathcal{O}(1)$ coefficients. In this framework, the structures of the Dirac neutrino Yukawa couplings and right-handed neutrino masses are determined entirely by the symmetry. The baryon asymmetry of the Universe is computed taking into account the flavor effects, Higgs asymmetry contributions, and the impact of the second-lightest right-handed neutrino. While the predicted asymmetry is too small when all $\mathcal{O}(1)$ coefficients of the Dirac neutrino Yukawa couplings are set to unity, a moderate enhancement factor $r_1 \sim 5.4$ for the lightest right-handed neutrino mass reproduces the observed baryon asymmetry without spoiling low-energy neutrino data. This corresponds to a suppressed lightest neutrino mass, $m_{\nu_1} \sim (1/r_1) \times (\text{symmetry-determined value})$, typically $m_{\nu_1} \sim 4.5 \times 10^{-4}\,\text{eV}$. We further explore cases where the $\mathcal{O}(1)$ coefficients of the Dirac neutrino Yukawa couplings are $\pm 1$, and find that roughly half of them successfully generate the observed baryon asymmetry for $r_1\leq 11$. Moreover, the others yield results of the correct order of magnitude, although they do not generate the observed Baryon asymmetry. These findings demonstrate that thermal leptogenesis is realized in this $SO(10)\times U(1)_A$ SUSY GUT, establishing a link between the observed baryon asymmetry and predictions for the lightest neutrino mass.