Can the Supersymmetric $\mu$ parameter be generated dynamically without a light Singlet?

Abstract

It is generally assumed that the dynamical generation of the Higgs mass parameter of the superpotential, $\mu$, implies the existence of a light singlet at or below the supersymmetry breaking scale, $\text{msusy}$. We present a counter-example in which the singlet field can receive an arbitrarily heavy mass (\eg, of the order of the Planck scale, $M_{\mathrm{P}}\approx 10^{19}\text{gev}$). In this example, a non-zero value of $\mu$ is generated through soft supersymmetry breaking parameters and is thus naturally of the order of $\text{msusy}$.

Comments: 6 pages, phyzzx, DESY 94-061