$\mu$ Problem, SO(10) SUSY GUT and Heavy Gluino LSP

Abstract

We present a solution to the $\mu$ problem in an SO(10) supersymmetric grand unified (SUSY GUT) model with gauge mediated (GMSB) and D-term supersymmetry breaking. A Peccei-Quinn ({\bf PQ}) symmetry is broken at the messenger scale and enables the generation of the $\mu$ term. The invisible axion (Goldstone boson of {\bf PQ} symmetry breaking) is a cold dark matter candidate. At low energy, our model leads to a phenomenologically acceptable version of the minimal supersymmetric standard model (MSSM) with novel particle phenomenology. Either the gluino or the gravitino is the lightest supersymmetric particle (LSP). The phenomenological constraints on the model result in a Higgs with mass $\sim 86 - 91$ GeV and $\tan\beta \sim 9 - 14$.