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

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We present a detailed study of the quark and lepton mass spectra in a SO(10) framework with one 10_H and one \bar{126}_H Higgs representations in the Yukawa sector. We consider in full generality the interplay between type-I and type-II seesaws for neutrino masses. We first perform a \chi^2 fit of fermion masses independent on the detailed structure of the GUT Higgs potential and determine the regions in 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 \bar{126}_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 is 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.
Phys.Rev. D73 (2006) 115012