Theory and Phenomenology of mu in M theory

Abstract

We consider a solution to the mu-problem within M theory on a G2-manifold. Our study is based upon the discrete symmetry proposed by Witten that forbids the mu-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 mu-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 - 30 TeV. We show that mu is suppressed relative to the gravitino mass, by higher dimensional operators, mu ~ 0.1 m_{3/2} ~ 2-3 TeV. 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.