The $SO(10)$-inspired leptogenesis timely opportunity

We study the connection between absolute neutrino mass and neutrino mixing parameters within $SO(10)$-inspired leptogenesis. We show that current favoured values of the unknown neutrino mixing parameters point toward values of the absolute neutrino mass scale that will be fully tested by cosmological observations and neutrinoless double beta decay experiments during next years. In particular, for $m_{D2}/m_{\rm charm} \leq 5$, where $m_{D2}$ is the intermediate Dirac neutrino mass, and for current best fit values of the Dirac phase $\delta$ and the atmospheric neutrino mixing angle $\theta_{23}$, we derive a lower bound on the neutrinoless double beta decay effective neutrino mass $m_{ee} \gtrsim 31\,{\rm meV}$ and on the sum of the neutrino masses $\sum_i m_i \gtrsim 125\,{\rm meV}$. These lower bounds hold for normally ordered neutrino masses, as currently favoured by global analyses and approximately for $\delta \in [155^\circ,240^\circ]$ and $\theta_{23}$ in the second octant. If values in this region will be confirmed by future planned long baseline experiments, then a signal at next generation neutrinoless double beta decay experiments is expected, despite neutrino masses being normally ordered. Outside the region, the lower bounds strongly relax but a great fraction of the allowed range of values still allows a measurement of the lightest neutrino mass. Therefore, in the the next years low energy neutrino experiments will provide a very stringent test of $SO(10)$-inspired leptogenesis, resulting either in severe constraints or in a strong evidence.