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

TL;DR

This work shows that thermal leptogenesis can be realized in a natural $SO(10)\times U(1)_A$ GUT, where all symmetry-allowed operators carry O(1) coefficients and the Dirac neutrino Yukawas and RH-neutrino masses are fixed by the flavour symmetry. By including flavor effects, spectator contributions, and the role of the second-lightest RH neutrino, the authors find that the observed baryon asymmetry is reproduced when the lightest RH neutrino mass is enhanced by a factor $r_1\approx5.4$, yielding $M_1\approx1.4\times10^9$ GeV and a predicted lightest neutrino mass $m_{\nu_1}\approx4.5\times10^{-4}$ eV. The analysis reveals that $N_2$-driven dynamics and flavor decoherence are crucial for successful leptogenesis, and that among 15 sign-patterns of the Dirac Yukawa coefficients, several patterns can accommodate the observed asymmetry for moderate $r_1$, highlighting a concrete link between high-scale GUT textures and low-energy neutrino parameters. A comparison with an $E_6\times U(1)_A$ variant shows the $SO(10)$ scenario typically yields a larger baryon asymmetry due to its CP-violating structure. These results establish a robust connection between the baryon asymmetry of the universe and predictions for the lightest neutrino mass within this natural GUT framework.

Abstract

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, $m_{ν_1} \sim (1/r_1) \times (\text{symmetry-determined value})$, typically $m_{ν_1} \sim 4.5 \times 10^{-4}\,\text{eV}$. 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.

Figures (5)

• Figure 1: $r_1$ dependence of $Y_{B-L}$ for (a) $N_1+N_2$ with the flavor effect, (b) $N_1+N_2$ without the flavor effect, (c) $N_1$ only with the flavor effect, (d) $N_1$ only without the flavor effect.
• Figure 2: $Y_{B-L}$ evolutions for $N_1+N_2$ (blue solid), for $N_2$ only (blue dashed), and for $N_1$ only (yellow dashed). This calculation does not take the flavor effect into account. Gray band indicates the range of $B-L$ asymmetry required to reproduce the observed baryon asymmetry.
• Figure 3: Evolutions of $Y_{B-L}$ and each flavor contribution for $r_1 = 1$ (a) and $5.4$ (b). Gray band indicates the range of $B-L$ asymmetry required to reproduce the observed baryon asymmetry.
• Figure 4: The $r_1$ dependence of flavored $Y_{B-L}$ in four cases: (a)pattern 0, (b)pattern 1, (c)pattern 3, and (d)pattern 5. The absolute value of total $Y_{B-L}$ represents thick solid line. The thin solid lines denote negative $Y_{\Delta_\alpha}$ in Figures (b), (c), and (d), while the dotted, dot-dashed, and dashed lines denote the positive $Y_{\Delta_\alpha}$.
• Figure 5: Evolution of $Y_{B-L}$ in the $SO(10) \times U(1)_A$ and $E_6 \times U(1)_A$ scenarios. We set $r_1=1$ in the $N_1+N_2$ framework including flavor effects. The grey band denotes the required $B-L$ asymmetry to account for the observed baryon asymmetry.