Dimensionless supersymmetry breaking couplings, flat directions, and the origin of intermediate mass scales

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Abstract
The effects of supersymmetry breaking are usually parameterized by soft couplings of positive mass dimensions. However, realistic models also predict the existence of suppressed, but non-vanishing, dimensionless supersymmetry-breaking couplings. These couplings are technically hard, but do not lead to disastrous quadratic divergences in scalar masses, and may be crucial for understanding low-energy physics. In particular, analytic scalar quartic couplings that break supersymmetry can lead to intermediate scale vacuum expectation values along nearly-flat directions. I study the one-loop effective potential for flat directions in the presence of dimensionless supersymmetry-breaking terms, and discuss the corresponding renormalization group equations. I discuss two applications: a minimal model of automatic R-parity conservation, and an extension of this minimal model which provides a solution to the \mu problem and an invisible axion.
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