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)(L) circle times SU(N)(R) circle times Q. Proton decay lifetime constrains the unification scale to be greater than or similar to 10(16) GeV and. as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is greater than or similar to 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 nonsupersymmctric (non-SUSY) versions arc considered. In addition to the fermion and scalar representations at each stage of the symmetry breaking, contributing to the beta functions, we list the intemiediate 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 similar to 10(12) GeV, for the SUSY scale to be similar to 30 TeV. This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter.