Strong thermal $SO(10)$-inspired leptogenesis in the light of recent results from long-baseline neutrino experiments

We confront recent experimental results on neutrino mixing parameters with the requirements from strong thermal $SO(10)$-inspired leptogenesis, where the asymmetry is produced from next-to-lightest right-handed neutrinos $N_2$ independently of the initial conditions. There is a nice agreement with latest global analyses supporting $\sin\delta < 0$ and normal ordering at $ \sim 95\%$ C.L. On the other hand, the more stringent experimental lower bound on the atmospheric mixing angle starts to corner strong thermal $SO(10)$-inspired leptogenesis. Prompted and encouraged by this rapid experimental advance, we obtain a precise determination of the allowed region in the plane $\delta$ versus $\theta_{23}$. We confirm that for the benchmark case $\alpha_2 \equiv m_{D2} / m_{\rm charm}= 5 \, $, where $m_{D2}$ is the intermediate neutrino Dirac mass setting the $N_2$ mass, and initial pre-existing asymmetry $N_{B-L}^{\rm p, i} = 10^{-3}$, the bulk of solutions lies in the first octant. Though most of the solutions are found outside the $95\%$ C.L. experimental region, there is still a big allowed fraction that does not require a too fine-tuned choice of the Majorana phases so that the neutrinoless double beta decay effective neutrino mass allowed range is still $m_{ee}\simeq [10,30]\,{\rm meV}$. We also show how the constraints depend on $N_{B-L}^{\rm p, i}$ and $\alpha_2$. In particular, we show that the current best fit, ($\theta_{23},\delta)\simeq (47^{\circ}, -130^{\circ})$, can be reproduced for $N_{B-L}^{\rm p, i} = 10^{-3}$ and $\alpha_2 = 6$. Such large values for $\alpha_2$ have been recently obtained in a few realistic fits within $SO(10)$-inspired models. Finally, we also obtain that current neutrino data rule out $N_{B-L}^{\rm p, i} \gtrsim 0.1$ for $\alpha_2 \lesssim 4.7$.