Mass-Splitting between Haves and Have-Nots (Symmetry vs. Grand Unified Theory)

TL;DR

This paper addresses the doublet-triplet splitting problem in supersymmetric GUTs, proposing a symmetry-breaking mechanism that naturally separates Higgs doublets and triplets, demonstrated through an SU(5)×SU(5) model.

Contribution

It introduces a novel symmetry-breaking approach to achieve doublet-triplet splitting, compatible with GUT-scale physics and low-energy supersymmetry.

Findings

Successful construction of an SU(5)×SU(5) GUT model implementing the mechanism.

Demonstration that the symmetry controlling the {} term must be broken at the GUT scale.

Discussion on the unification of Yukawa couplings within the proposed framework.

Abstract

We revisit the long-standing problem of supersymmetric grand unified theory (GUT), the doublet-triplet splitting problem. We discuss whether symmetry which controls the {\mu} term in the minimal supersymmetric standard model is compatible with GUT. We find that the symmetry must be broken at the GUT scale. A similar argument also shows that the R symmetry, which is important for low energy supersymmetry, must be broken down to a Z2R symmetry at the GUT scale. We propose a new prescription to achieve the doublet-triplet splitting by symmetry. There, the symmetry which controls the {\mu} term is spontaneously broken at the GUT scale by order parameters which are charged under other symmetries. Bilinear terms of triplet Higgses are charged under the other symmetries, while those of doublet Higgses are not. Then triplet Higgses directly couple to the order parameters and hence obtain GUT scale masses, while doublet Higgses obtain suppressed masses. The broken R symmetry can be also effectively preserved by a similar prescription. As a demonstration, we construct an SU(5)$\times$SU(5) GUT model. We also comment on unification of yukawa couplings.