Solution to the μ problem in the presence of a heavy gluino LSP

In this paper we present a solution to the μ problem in an SO(10) supersymmetric grand unified model with gauge mediated and D-term supersymmetry breaking. Peccei-Quinn symmetry is broken at the messenger scale $M\sim {10}^{12}\hspace{0.5em}\mathrm{GeV}$ and enables the generation of the μ term. The boundary conditions defined at M lead to a phenomenologically acceptable version of the minimal supersymmetric standard model with novel particle phenomenology. Either the gluino or the gravitino is the lightest supersymmetric particle (LSP). If the gravitino is the LSP, then the gluino is the next-to-LSP (NLSP) with a lifetime on the order of one month or longer. In either case this heavy gluino, with a mass in the range 25–35 GeV, can be treated as a stable particle with respect to experiments at high energy accelerators. Given the extensive phenomenological constraints we show that the model can only survive in a narrow region of parameter space resulting in a light neutral Higgs boson with a mass $\sim (86\mathrm{}–91)\pm 6\hspace{0.5em}\mathrm{GeV}$ and $\tan \beta \sim 9–14.$ In addition the lightest top squark and neutralino have masses $\sim 100–122\hspace{0.5em}\mathrm{GeV}$ and $\sim 50–72\hspace{0.5em}\mathrm{GeV},$ respectively. Thus the model will soon be tested. Finally, the invisible axion resulting from Peccei-Quinn symmetry breaking is a cold dark matter candidate.