Neutrino masses, $δ_\mathrm{PMNS}$, and $m_{ββ}$ in SO(10)

TL;DR

This work analyzes the leptonic sector of a SUSY SO(10) model with SUSY breaking at the multi-TeV scale under the requirement that the baryon asymmetry arises from non-thermal leptogenesis. It implements a SUSY hybrid inflation framework with higher-dimensional Higgs representations and a minimal Higgs sector, performing a χ^2 fit and subsequent MCMC to predict neutrino masses, the PMNS phase, and the neutrinoless double beta decay parameter, while connecting inflaton dynamics to leptogenesis. The results yield a lightest neutrino mass $m_1$ in the few meV range, heavy right-handed neutrino masses $M_1\approx1.8\times10^9$ GeV and $M_{2,3}\approx(7.4-7.8)\times10^{12}$ GeV, a best-fit leptonic CP phase $δ_{\mathrm{PMNS}}\approx235^\circ$, and $m_{\beta\beta}\approx0.18$ meV, with $m_\chi\approx7.29\times10^9$ GeV and $T_{\mathrm{RH}}\approx4.08\times10^6$ GeV. The analysis remains consistent with JUNO's reactor-oscillation measurements and gravitino constraints, while allowing $δ_{\mathrm{PMNS}}$ to vary broadly in $100^\circ$–$300^\circ$. These findings illustrate a consistent link between GUT-scale flavor structure, leptogenesis, and low-energy neutrino phenomenology.

Abstract

We explore the leptonic sector of a recently proposed supersymmetric SO(10) model with supersymmetry breaking in the 3-10 TeV range. A new ingredient in this work is the requirement that the observed baryon asymmetry is explained via non-thermal leptogenesis, which can be realized in a large class of supersymmetric hybrid inflation models including SO(10). We provide estimates for the masses of the three Standard Model neutrinos (with the lightest mass $m_1\approx 5$ meV) as well as the three right-handed neutrinos ($M_1\approx 10^9$ GeV and $M_{2,3}\approx 10^{13}$ GeV). The best fit estimate for the leptonic CP violating parameter $δ_\mathrm{PMNS}\approx 235^\circ$, and the value of the neutrinoless double beta decay mass parameter $m_{ββ}\approx 0.18$ meV. A numerical analysis broadens the predicted range for $δ_\mathrm{PMNS}$ ($100^\circ$-$300^\circ$), but leaves largely intact the predictions for the six (light and heavy) neutrino masses and $m_{ββ}$. Our statistical analysis, which yields the likelihood-predicted ranges of the observables, is fully consistent with JUNO's newly released first measurement of reactor neutrino oscillations in the $Δm^2_{12}$-$\sin^2θ_{12}$ plane, with JUNO improving the precision by a factor of 1.6 relative to the combination of all previous measurements. The implementation of successful non-thermal leptogenesis allows us to provide estimates for the inflaton mass ($m_χ\approx 7\times 10^{9}$ GeV) and the reheating temperature ($T_\mathrm{RH}\approx 4\times 10^6$ GeV).

Figures (9)

• Figure 1: Third generation Yukawa couplings at $M_\mathrm{GUT}=2\times 10^{16}$ GeV, as a function of $\tan\beta$ for $M_\mathrm{SUSY}=3$ TeV, ignoring threshold corrections. $t\!-\!b$ Yukawa unification occurs at $\tan\beta \sim 58.9$ (red dashed vertical line), whereas $t\!-\!\tau$ unification corresponds to $\tan\beta \sim 51.56$ (blue dashed vertical line).
• Figure 2: The left panel shows, for the best fit (that has $\epsilon_1=-2.87\times 10^{-7}$), the inflaton mass $m_\chi$ consistent with correctly reproducing the baryon asymmetry. The corresponding reheating temperature $T_\mathrm{RH}$ is shown in the right panel as a function of $m_\chi$ (where $T_{\mathrm{RH}} \approx 4 \times 10^{6}\,\mathrm{GeV}$ is compatible with the observed baryon asymmetry). In the gray shaded region the inflaton decay into $N_1$ is kinematically forbidden. The horizontal yellow band shows a 10% variation of the baryon asymmetry parameter around its central value.
• Figure 3: MCMC result: The likelihood range of $\delta_\mathrm{PMNS}\in (100,300)^\circ$--compatible with fermion masses and baryon asymmetry with the correct sign and magnitude. Although we have shown the $1\sigma$ range of $\delta_\mathrm{PMNS}$ from NuFit, the $3\sigma$ range spans a much wider interval of $96^\circ - 422^\circ$NUFIT. The red star corresponds to the best fit solution ($\delta_\mathrm{PMNS}=235^\circ$).
• Figure 4: MCMC result. Left panel: Compatibility of our results with the new JUNO result JUNO:2025gmd. Right panel: The likelihood range of neutrinoless double beta decay as a function of the lightest neutrino mass. The current bound from KamLAND-Zen KamLAND-Zen:2016pfg and the future sensitivities of next-generation experiments, such as GERDA Phase II GERDA:2019cav and nEXO nEXO:2021ujk, as well as JUNO's 50-ton sensitivity after 5 years of operation Zhao:2016brs, are shown. Best fit corresponds to $m_1=5.12$ meV and $m_{\beta\beta}=0.18$ meV.
• Figure 5: MCMC result: The likelihood distribution of light (heavy) neutrino masses in the left (right) panel. The lightest SM neutrino mass is predicted to be in the range $m_1\sim (2-7)$ meV. In the right panel, the overlapping region with $M_3>M_2$ is indicated by the darker color.