Roadmap of left-right models based on GUTs

TL;DR

This paper provides a comprehensive analysis of grand unified theories based on $SO(10)$ and $E(6)$, exploring how different symmetry breaking patterns and scales impact unification, proton decay constraints, and supersymmetry phenomenology.

Contribution

It systematically studies all viable left-right models within $SO(10)$ and $E(6)$ GUT frameworks, including SUSY and non-SUSY scenarios, with detailed renormalization group analysis and unification conditions.

Findings

Proton decay constrains unification scale to above 10^{16} GeV.

Intermediate symmetry scales can be as low as 10^{12} GeV under certain conditions.

In SUSY models, SUSY breaking scale must be at least a few TeV for successful unification.

Abstract

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}$ GeV and, as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is $ \gtrsim 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 Non-supersymmetric (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 which 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 $\sim 10^{12}$ GeV, for SUSY scale to be $\sim 30$ TeV. This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter.