# Effective Higgs Theories in Supersymmetric Grand Unification

## TL;DR

This paper systematically derives effective Higgs theories at the TeV scale within supersymmetric $SU(5)$ grand unification, identifying models consistent with perturbative unification and analyzing their experimental viability.

## Contribution

It classifies the possible Higgs sector extensions in supersymmetric $SU(5)$ models and assesses their compatibility with perturbative grand unification and experimental data.

## Key findings

- Only two types of vector-like models are consistent with perturbative unification.
- The chiral model is excluded by LHC data.
- The future of unification depends on the vector-like models identified.

## Abstract

The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand unification models are systematically derived. Restricted to extensions on $\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of real (vector-like) models and one type of chiral model are found to be consistent with perturbative grand unification. While the chiral model has been excluded by the LHC data, the fate of perturbative unification will be uniquely determined by the two classes of vector-like models.