Type II Seesaw Dominance in Non-supersymmetric and Split Susy SO(10) and Proton Life Time

Recently type II seesaw dominance in a supersymmetric SO(10) framework has been found useful in explaining large solar and atmospheric mixing angles as well as larger values of $theta_{13}$ while unifying quark and lepton masses. An important question in these models is whether there exists consistency between coupling unification and type II seesaw dominance. Scenarios where this consistency can be demonstrated have been given in a SUSY framework. In this paper we give examples where type II dominance occurs in SO(10) models without supersymmetry but with additional TeV scale particles and also in models with split-supersummetry. Grand unification is realized in a two-step process via breaking of SO(10) to SU(5) and then to a TeV scale standard model supplemented by extra fields and an SU(5) Higgs multiplet ${15}_H$ at a scale about $10^{12}$ GeV to give type-II seesaw. The predictions for proton lifetime in these models are in the range $\tau_p^0 = 2\times 10^{35}$ yrs. to $\tau_p^0 = 6\times 10^{35}$ yrs.. A number of recent numerical fits to GUT-scale fermion masses can be accommodated within this model.