Realization of the large mixing angle solar neutrino solution in anSO(10)supersymmetric grand unified model

An $\mathrm{SO}\left(10\right)\mathrm{}$ supersymmetric grand unified model proposed earlier leading to the solar solution involving “just-so” vacuum oscillations is reexamined to study its ability to obtain the other possible solar solutions. It is found that all four viable solar neutrino oscillation solutions can be achieved in the model simply by modification of the right-handed Majorana neutrino mass matrix $M_R.$ Whereas the small mixing and vacuum solutions are easily obtained with several texture zeros in $M_R,$ the currently favored large mixing angle solution requires a nearly geometric hierarchical form for $M_R$ that leads by the seesaw formula to a light neutrino mass matrix which has two or three texture zeros. The form of the matrix which provides the “fine-tuning” necessary to achieve the large mixing angle solution can be understood in terms of Froggatt-Nielsen diagrams for the Dirac and right-handed Majorana neutrino mass matrices. The solution satisfies several leptogenesis requirements which in turn can be responsible for the baryon asymmetry in the universe.