Lepton Mixing and Cancellation of the Dirac Mass Hierarchy in SO(10)   GUTs with Flavor Symmetries T7 and Sigma(81)
  In SO(10) grand unified theories (GUTs) the hierarchy which is present in the Dirac mass term of the neutrinos is generically as strong as the one in the up-type quark mass term. We propose a mechanism to partially or completely cancel this hierarchy in the light neutrino mass matrix in the seesaw context. The two main ingredients of the cancellation mechanism are the existence of three fermionic gauge singlets and of a discrete flavor symmetry G_f which is broken at a higher scale than SO(10). Two realizations of the cancellation mechanism are presented. The realization based on the Frobenius group T7 = Z7 x Z3 leads to a partial cancellation of the hierarchy and relates maximal 2-3 lepton mixing with the geometric hierarchy of the up-quark masses. In the realization with the group Sigma(81) the cancellation is complete and tri-bimaximal lepton mixing is reproduced at the lowest order. In both cases, to fully accommodate the leptonic data we take into account additional effects such as effects of higher-dimensional operators involving more than one flavon. The heavy neutral fermion mass spectra are considered. For both realizations we analyze the flavon potential at the renormalizable level as well as ways to generate the Cabibbo angle. 
Claudia Hagedorn, Michael A. Schmidt, Alexei Yu. Smirnov