Roadmap of left-right models based on GUTs

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.