Minimal Nambu-Goldstone Higgs Model in Supersymmetric SU(5) Revisited

TL;DR

This paper revisits a supersymmetric SU(5) grand unified model with a Nambu-Goldstone Higgs, highlighting its natural light Higgs doublets, predictive couplings, and implications for proton decay and gaugino mass hierarchies.

Contribution

It provides a detailed phenomenological analysis of the minimal Nambu-Goldstone Higgs SUSY SU(5) model, including parameter determination and experimental constraints, emphasizing its viability in high-scale SUSY scenarios.

Findings

Model naturally solves doublet-triplet splitting.

Proton lifetime predictions are testable with future experiments.

Hierarchical gaugino mass pattern is implied by perturbativity constraints.

Abstract

We revisit the minimal Nambu-Goldstone (NG) Higgs supersymmetric (SUSY) SU(5) grand unified model and study its phenomenological implications. The Higgs sector of the model possesses a global SU(6) symmetry, which is spontaneously broken and results in the Higgs doublets of the minimal SUSY Standard Model (MSSM) as NG chiral superfields. Therefore, the model naturally leads to light Higgs doublets and solves the doublet-triplet splitting problem. Because of the SU(6) symmetry, the couplings of the Higgs sector are tightly restricted, and thus the model is more predictive than the minimal SUSY SU(5). We determine all the grand-unified-theory parameters via the matching conditions of the gauge coupling constants at the unification scale and calculate proton lifetime, confronting this with current experimental bounds. We discuss that this model is incompatible with the constrained MSSM, whilst it has a large viable parameter space in the high-scale SUSY scenario. The perturbativity condition on the trilinear coupling of the adjoint Higgs field imposes an upper (lower) limit on the wino (gluino) mass, implying a hierarchical mass pattern for these gauginos. Future proton-decay searches can probe a large part of the parameter space, especially if the SUSY-breaking scale is $\lesssim 100$~TeV.