We perform a detailed study of the grand unified theories $SO(10)$ and $E(6)$ with left-right intermediate gauge symmetries of the form $SU(N{)}_L\otimes SU(N{)}_R\otimes \mathcal{G}$. Proton decay lifetime constrains the unification scale to be $\gtrsim {10}^{16}\mathrm{GeV}$ and, as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is $\gtrsim {10}^{12}\mathrm{GeV}$. 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 $\beta$ 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 $\sim {10}^{12}\mathrm{GeV}$, for the SUSY scale to be $\sim 30\mathrm{TeV}$. This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter.

• Received 4 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.095010

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Published by the American Physical Society