Unification Predictions With or Without Supersymmetry (2002.06869v2)

Abstract: Supersymmetric (SUSY) grand unified theories (GUTs) appear to be best motivated for understanding strong, weak and electromagnetic interactions of nature. We briefly review emergence of new formulas for running fermion masses valid in direct breaking of GUTs. High scale mixing unification of quark and neutrino mixings and existence of theorems on vanishing theoretical uncertainties in GUT predictions are discussed. D-Parity properties of SO(10) representations leading to large number of intermediate breaking models are pointed out. Unification predictions of SUSY SO(10) in the light of neutrino mass, lepton flavor violation, baryogenesis via leptogenesis within gravitino constraint, and proton decay are noted. We further discuss realisation of flavour unification and possibility of fitting all fermion masses through R-Parity and D-Parity conserving left-right symmetric intermediate breaking in SUSY SO(10)$\times S_4$. In the absence of SUSY two interesting possibilities of minimal grand desert modifications with only one intermediate mass scalar in each case and their applications to dark matter decay through type-I seesaw are briefly noted. Heavy scalar triplet decay leptogenesis through new ansatz for type-II seesaw dominance in non-SUSY SO(10), emergence of new CP asymmetry formulas and model capabilities to explain WIMP dark matter, vacuum stability of the scalar potential and experimentally observed limit on proton lifetime are briefly summarized.