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

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 $\delta_\mathrm{PMNS}\approx 235^\circ$, and the value of the neutrinoless double beta decay mass parameter $m_{\beta\beta}\approx 0.18$ meV. A numerical analysis broadens the predicted range for $\delta_\mathrm{PMNS}$ ($100^\circ$-$300^\circ$), but leaves largely intact the predictions for the six (light and heavy) neutrino masses and $m_{\beta \beta}$. 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 $\Delta m^2_{12}$-$\sin^2\theta_{12}$ 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 ($m_\chi \approx 7\times 10^{9}$ GeV) and the reheating temperature ($T_\mathrm{RH}\approx 4\times 10^6$ GeV).