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We perform a detailed study of the grand unified theories SO (10) and E (6) with left-right intermediate gauge symmetries of the form SU (N) ₋ (N) ₑ. Proton decay lifetime constrains the unification scale to be 10^16 GeV and, as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is 10^12 GeV. With these conditions, we study the renormalization group evolution of the gauge couplings and do a comparative analysis of all possible left-right models where unification can occur. Both the D-parity conserved and broken scenarios as well as the supersymmetric (SUSY) and nonsupersymmetric (non-SUSY) versions are considered. In addition to the fermion and scalar representations at each stage of the symmetry breaking, contributing to the functions, we list the intermediate left-right groups that successfully meet these requirements. We make use of the dimension-5 kinetic mixing effective operators for achieving unification and large intermediate scale. A significant result in the supersymmetric case is that to achieve successful unification for some breaking patterns, the scale of SUSY breaking needs to be at least a few TeV. In some of these cases, the intermediate scale can be as low as 10^12 GeV, for the SUSY scale to be 30 TeV. This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter.
Chakrabortty et al. (Wed,) studied this question.
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