SO(10) grand unification in five dimensions: Proton decay and the mu problem

We construct a minimal supersymmetric SO(10) grand unified model in 5 dimensions. The extra dimension is compactified on an S^1/(Z_2 x Z_2^\prime) orbifold which has two in-equivalent fixed points. These are flat 4-dimensional Minkowski spaces: the visible and the hidden branes. By orbifolding, the gauge symmetry on the hidden brane is reduced down to the Pati--Salam gauge symmetry SU(4) x SU(2)_L x SU(2)_R. On the visible brane the SO(10) is broken by the ordinary Higgs mechanism down to SU(5). The resulting 4-dimensional theory has the standard model gauge symmetry (the intersection of SU(5) and SU(4) x SU(2)_L x SU(2)_R) and the massless spectrum consists of the MSSM gauge fields and two Higgs doublets. The matter fields are assumed to live on the visible brane. We discuss gauge coupling unification in our 5-dimensional model in terms of corrections to the conventional 4-dimensional unification. Supersymmetry is broken on the hidden brane (where mass terms for gauginos and a mu term are generated) and communicated to squarks and sleptons via gaugino mediation. We also discuss a possibility of linking the supersymmetry breaking on the hidden brane to the Higgs mechanism responsible for partial breaking of the gauge symmetry on the visible brane via the shining mechanism. Finally, there are no operators of dimension 5 leading to proton decay. Proton decay through dimension 6 operators is enhanced compared to conventional GUTs and can be seen in current or next generation proton decay experiments