Grand unification and intermediate scale supersymmetry

With minimal field content and for an interesting range of the supersymmetric Higgs mixing parameter, 0.5 ≲ tan2β ≲ 2, the superpartner mass scale, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \tilde{m} $\end{document}, is found to be at the intermediate scale, ~ 1010±1 GeV, near where the Standard Model Higgs quartic coupling passes through zero. For any 4d supersymmetric grand unified symmetry spontaneously broken by a vacuum expectation value 〈Σ〉, if superpotential interactions for Σ are forbidden e.g. by R symmetries, the uneaten color octet, Σ8, and weak triplet, Σ3, have masses of order m. The combination of superpartner and Σ8,3 states leads to successful gauge coupling unification, removing the disastrously high proton decay rate of minimal Standard Model unification. Proton decay could be seen in future experiments if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \tilde{m} $\end{document} ~ 1011 GeV,but not if it is lower. If there heating temperature after inflation, TR, is less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \tilde{m} $\end{document} dark matter may be axions. If TR > \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \tilde{m} $\end{document}, thermal LSP dark matter may lead to the environmental selection of a TeV-scale LSP, either wino or Higgsino, which could comprise all or just one component of dark matter. In the Higgsino case, the dark matter is found to behave inelastically in direct detection experiments, and gauge coupling unification occurs accurately without the need of any threshold corrections.