Fine-tuning and the doublet-triplet splitting problem in the minimal $SU(5)$ GUT

Abstract

In this paper we analyse the doublet-triplet splitting problem in the minimal non-supersymmetric SU (5) GUT. We take into account the full symmetry breaking pattern with both high scale SU (5) breaking and electroweak symmetry breaking. Our analysis shows that the only acceptable model has three vevs, with a hierarchy imposed by the minimization conditions. The amount of fine-tuning in the model is then determined by looking at both the minimization conditions and the bosonic masses. We find no indication for fine-tuning in this scenario. Therefore we conclude that doublet-triplet splitting is not a fundamental problem in this model.