Theory and Phenomenology of mu in M theory

TL;DR

This paper explores a solution to the mu-problem in M theory on G2-manifolds, detailing how symmetry breaking and moduli stabilization generate a suppressed mu-term, influencing dark matter properties and detection prospects.

Contribution

It presents a novel mechanism for mu-term generation in M theory that links symmetry breaking, moduli stabilization, and supersymmetry breaking effects.

Findings

Mu is suppressed relative to the gravitino mass, approximately 0.1 m_{3/2}.

The resulting LSP has a Higgsino component affecting dark matter detection.

Predicted cross-sections are below current experimental limits but accessible in future experiments.

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.