Perturbative unification of gauge couplings in supersymmetric $E_6$ models

Abstract

We study gauge coupling unification in supersymmetric $E_6$ models where an additional $\mathrm{U}(1{)}^{\prime }$ gauge symmetry is broken near the TeV scale and a number of exotic matter fields from the $27$ representations have $O(\mathrm{TeV})$ mass. Solving the 2-loop renormalization group equations of gauge couplings and a kinetic mixing coupling between the $\mathrm{U}(1{)}^{\prime }$ 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.

Comments: 10 pages, 2 figures, version to appear in MPLA