Supersymmetry with Small mu: Connections between Naturalness, Dark Matter, and (Possibly) Flavor

Weak scale supersymmetric theories often suffer from several naturalness problems: the problems of reproducing the correct scale for electroweak symmetry breaking, the correct abundance for dark matter, and small rates for flavor violating processes. We argue that the first two problems point to particular regions of parameter space in models with weak scale supersymmetry: those with a small mu term. This has an interesting implication on direct dark matter detection experiments. We find that, if the signs of the three gaugino mass parameters are all equal, we can obtain a solid lower bound on the spin-independent neutralino-nucleon cross section, \sigma. In the case that the gaugino masses satisfy the unified mass relations, we obtain \sigma > 4 x 10^{-46} cm^2 (1 x 10^{-46} cm^2) for fine-tuning in electroweak symmetry breaking no worse than 10% (5%). We also discuss a possibility that the three problems listed above are all connected to the hierarchy of fermion masses. This occurs if supersymmetry breaking and electroweak symmetry breaking (the Higgs fields) are coupled to matter fields with similar hierarchical structures. The discovery of mu -> e transition processes in near future experiments is predicted in such a framework.