Neutron-antineutron oscillations and SO (10) grand unification

Within the framework of the survival hypothesis for Higgs scalars we comprehensively examine the following question: could there be neutron-antineutron oscillations in SO(10) grand unified theories which would be detectable in the forthcoming experiments? In the process of answering this, we critically discuss and supplement the existing knowledge of the relevant patterns of SO(10) symmetry breakdown in relation to the said oscillations. However, our conclusions are negative with the oscillation period being 10²⁵ years or higher.     

SO(18) unification of fermion generations

We discuss the mass spectrum of light fermions in a recently proposed SO(18) model for family unification. We find that an intermediate B-L violating scale in the range of 10³ TeV provides a proper understanding of light neutrino (v_e, v_μ, v_τ, …) masses as well as the masses of their mirror partners. In this scenario, we expect at most four mirror neutrinos in the 2–10 GeV range, which could contribute to the width of the Z boson.     

Hierarchical fermion masses from grand unification

A mechanism is presented for generating fermion masses as a reflection of the superheavy fermions existing in a class of grand unified theories. By means of it we propose a way of understanding how, giving a driving mass term for the top-generation, the charm-generation mass results as a relative first-order perturbation in the unified gauge coupling g²/4π ≈ 10^?2, and the up-generation mass as a second-order perturbation. An illustrative calculation of the charm-generation mass is described in a model based on E₆.     

Four-dimensional heterotic string models with SU(5) and SO(10) grand unification

The gauge group, quark and lepton generations, Higgs scalar structure, couplings of quarks and leptons to Higgs scalars and to colour triplet scalars, and the gauge symmetry breaking are studied for a class of four-dimensional heterotic string models whose boundary conditions include third-integral twists.     

Radiative see-saw formula in nonsupersymmetric SO(10) with dark matter

In SO(10), the type-I and type-II see-saw scales ???10¹² GeV are far away from being probed by direct experimental tests. In the absence of supersymmetry, we show how experimentally verifiable radiative see-saw formula of Ma type is realized in non-SUSY SO(10) while fulfilling the twin objectives: precision gauge coupling unification and dark matter. This model is expected to have a dramatic impact on neutrino physics, dark matter and all fermion masses and mixings.     

SO(10) v ×SO(10) H grand unified-extended technicolour models

We discuss a recently proposedSO(10) _v ×SO(10) _H grand unified-extended technicolour model. Because proton decay is probably too fast in this model, we study the other possible models based onSO(10) _v ×SO(10) _H . As a result of this analysis only a few of these models could possibly be realistic, they would be slight modifications of that previously proposed. None of them predicts the expected value forΛ _TC, it must be adjusted by introducing another mass scale. In these models ordinary fermion masses tend to be too small.     

Higgs bosons in SO(10) and partial unification

The implications of the existence of a partial unification, previous to the grand unification into SO(10) are studied. Special emphasis is given to the influence of the Higgs bosons in the theory. We calculate their contribution to the β-functions of the partialunification roups of most phenomenological interest and it is found that the results previously calculated for the partial and grand unification masses are in general drastically changed. After making an extended “survival hypothesis” about the masses of the Higgses, we find that the partial unification mass (PUM) should be typically 10^10?11 GeV. The masses of the neutrinos are related to the PUM and we obtain m_ντ ～ 1–10 eV. Neutron oscillations can appear, but at a negligible rate. Proton decay may occur at the expected rate, although in some models it is highly suppressed. The result for the ratio m_b/m_τ is smaller than in SU(5) and the simplest SO(10) version.