Theory and phenomenology of μ in M theory

We consider a solution to the μ-problem within M theory on a G ₂-manifold. Our study is based upon the discrete symmetry proposed by Witten that forbids the μ-term and solves the doublet-triplet splitting problem. We point out that the symmetry must be broken by moduli stabilization, describing in detail how this can occur. The μ-term is generated via Kahler interactions after strong dynamics in the hidden sector generate a potential which stabilizes all moduli and breaks supersymmetry with m_3/2 ̃ 20-30TeV. We show that μ is suppressed relative to the gravitino mass, by higher dimensional operators, μ tild; 0:1m_3/2 - 2-3TeV. This necessarily gives a Higgsino component to the (mostly Wino) LSP, and a small but non-negligible LSP-nucleon scattering cross-section. The maximum spin-independent cross-sections are not within reach of the current XENON100 experiment, but are within reach of upcoming runs and upgrades.