A full analytic solution of $SO(10)$-inspired leptogenesis

Recent encouraging experimental results on neutrino mixing parameters prompt further investigation on $SO(10)$-inspired leptogenesis and on the associated strong thermal solution that has correctly predicted a non-vanishing reactor mixing angle, it further predicts $\sin\delta \lesssim 0$, now supported by recent results at $\sim 95\%$ C.L., normally ordered neutrino masses and atmospheric mixing angle in the first octant, best fit results in latest global analyses. Extending a recent analytical procedure, we account for the mismatch between the Yukawa basis and the weak basis, that in $SO(10)$-inspired models is described by a CKM-like unitary transformation $V_L$, obtaining a full analytical solution that provides useful insight and reproduces accurately all numerical results, paving the way for future inclusion of different sources of theoretical uncertainties and for a statistical analysis of the constraints. We show how muon-dominated solutions appear for large values of the lightest neutrino mass in the range $(0.01$--$1)\,{\rm eV}$ but also how they necessarily require a mild fine tuning in the seesaw relation. For the dominant (and untuned) tauon-dominated solutions we show how, turning on $V_L \simeq V_{CKM}$, some of the constraints on the low energy neutrino parameters get significantly relaxed. In particular we show how the upper bound on the atmospheric neutrino mixing angle in the strong thermal solution gets relaxed from $\theta_{23} \lesssim 41^{\circ}$ to $\theta_{23} \lesssim 44^{\circ}$, an important effect in the light of the most recent NO$\nu$A, T2K and IceCube results.