# A solution for the doublet-triplet splitting in $SU(5)$

## TL;DR

This paper proposes a novel solution to the doublet-triplet splitting problem in supersymmetric $SU(5)$ by extending the gauge group to $SU(5) imes SU(5)$ and utilizing non-perturbative superpotentials to achieve the desired symmetry breaking and Higgs mass separation.

## Contribution

It introduces an $SU(5) imes SU(5)$ model with specific supermultiplets that naturally solve the doublet-triplet splitting issue without the drawbacks of previous sliding singlet models.

## Key findings

- Successfully achieves gauge symmetry breaking and Higgs triplet mass generation.
- Provides a mechanism avoiding the drawbacks of the sliding singlet model.
- Ensures the correct mass hierarchy for Higgs doublets and triplets.

## Abstract

We present a solution to the doublet-triplet splitting problem in supersymmetric $SU(5)$ by enlarging the group to $SU(5)\times SU(5)$ and by introducing two supermultiplets in the $(5,5)$ and $(\bar{5},\bar{5})$ representations of the extended group. The non-perturbative superpotential associated to this gauge group provides not only the correct gauge symmetry breaking but also the large mass for the Higgs triplets associated to massless Higgs doublet. The method has all the advantages of the sliding singlet model but without the drawbacks.