A NATURAL SOLUTION TO THE MU PROBLEM

We propose a simple mechanism for solving the mu-problem in the context of minimal low-energy supergravity models. This is based on the appearance of non-renormalizable couplings in the superpotential. In particular, if H1H2 is an allowed operator by all the symmetries of the theory, it is natural to promote the usual renormalizable superpotential W0 to W0+lambdaW0H1H2, yielding an effective mu parameter whose size is directly related to the gravitino mass once supersymmetry is broken (this result is maintained if H1H2 couples with different strengths to the various terms present in W0). On the other hand, the mu-term must be absent in W0, otherwise the natural scale for mu would be M(Pl). Remarkably enough, this is entirely justified in the SUGRA theories coming from superstrings, where mass terms for light fields are forbidden in the superpotential. We also analyze the SU (2) X U (1) breaking, finding that it takes place satisfactorily. Finally, we give a realistic example in which SUSY is broken by gaugino condensation where the mechanism proposed for solving the mu-problem can be gracefully implemented.