Supersymmetry-breaking through D-terms

Models in which supersymmetry is broken by the Fayet-Iliopoulos mechanism are reconsidered. The possibility that scalar quark and lepton masses might arise radiatively in such theories is explored. It is shown that in several interesting cases, these masses-squared are all negative. In grand-unified versions of these models, it is shown that the scale of SU(2) × U(1) breaking tends to be much larger than the scalar quark and lepton masses, i.e. that the hierarchy is unstable.