Perturbative unification of gauge couplings in supersymmetric $E_6$ models

TL;DR

This paper investigates gauge coupling unification in supersymmetric $E_6$ models with an extra $ ext{U}(1)'$ symmetry, analyzing the impact of exotic matter and threshold corrections on perturbativity up to the GUT scale.

Contribution

It provides a detailed 2-loop analysis of gauge coupling running in $E_6$ models, including kinetic mixing and threshold effects, to determine conditions for perturbative unification.

Findings

Gauge couplings become non-perturbative below the GUT scale without corrections.

Threshold corrections can restore perturbative unification under certain conditions.

Exotic matter at TeV scale influences the unification scenario.

Abstract

We study gauge coupling unification in supersymmetric $E_6$ models where an additional $\mathrm{U}(1)'$ gauge symmetry is broken near the TeV scale and a number of exotic matter fields from the $\bm{27}$ representations have $O(\mathrm{TeV})$ mass. Solving the 2-loop renormalization group equations of gauge couplings and a kinetic mixing coupling between the $\mathrm{U}(1)'$ and $\mathrm{U}(1)_Y$ gauge fields, we find that the gauge couplings fall into the non-perturbative regime below the GUT scale. We examine threshold corrections on the running of gauge couplings from both light and heavy ($\sim$ GUT scale) particles and show constraints on the size of corrections to achieve the perturbative unification of gauge couplings.