Fermion masses and mixings in SO(10) models and the neutrino challenge to supersymmetric grand unified theories

We present a detailed study of the quark and lepton mass spectra in a SO(10) framework with one 10(H) and one (126) over bar (H),one 126(H), and one 210(H) Higgs representations in the Yukawa sector. We consider in full generality the interplay between type I and type II seesaw for neutrino masses. We first perform a chi(2) fit of fermion masses independent on the structure of the GUT Higgs potential and determine the regions of the parameter space that are preferred by the fermion mass sum rules. We then apply our study to the case of the minimal renormalizable SUSY SO(10) GUT with one 10(H), one (126) over bar (H), one 126(H), and one 210(H) Higgs representations. By requiring that proton decay bounds are fulfilled we identify a very limited area in the parameter space where all fermion data are consistently reproduced. We find that in all cases gauge coupling unification in the supersymmetric scenario turns out to be severely affected by the presence of lighter than GUT (albeit B-L conserving) states. We then conclusively show that the minimal supersymmetric SO(10) scenario here considered is not consistent with data. The fit of neutrino masses with type I and type II seesaws within a renormalizable SO(10) framework strongly suggests a non-SUSY scenario for gauge unification.