New tools for low energy dynamical supersymmetry breaking

We report the construction of large new classes of models which break supersymmetry dynamically. We then turn to model building. Two of the principal obstacles to constructing simple models of dynamical supersymmetry breaking are the appearance of Fayet-Iliopoulos {ital D} terms and difficulties in generating a {mu} term for the Higgs fields. Among the new models are examples in which symmetries prevent the appearance of Fayet-Iliopoulos terms. A gauge singlet field, which may play a role in explaining the hierarchy in quark and lepton parameters, can generate a suitable {mu} term. The result is a comparatively simple model, with a low energy structure similar to that of the MSSM, but with far fewer arbitrary parameters. We begin the study of the phenomenology of these models. {copyright} {ital 1996 The American Physical Society.}