Minimal SUSY SO(10), b-$\tau$ unification and large neutrino mixings

We show that the assumption of type II seesaw mechanism for small neutrino masses coupled with $b-\tau$ mass unification in a minimal SUSY SO(10) model leads not only to a natural understanding of large atmospheric mixing angle ($\theta_{23}$) among neutrinos, as recently pointed out, but also to large solar angle ($\theta_{12}$) and a small $\theta_{13}\equiv U_{e3}$ as required to fit observations. This is therefore a minimal, completely realistic grand unified model for all low energy observations that naturally explains the diverse mixing patterns between the quark and leptons without any additional inputs such as extra global symmetries. The proposed long baseline neutrino experiments will provide a crucial test of this model since it predicts $U_{e3}\simeq 0.16$ for the allowed range of parameters.