Fayet-Iliopoulos D term and its renormalization in the minimal supersymmetric standard model

We consider the renormalization of the Fayet-Iliopoulos D term in a softly broken supersymmetric gauge theory with a nonsimple gauge group containing an Abelian factor, and present the associated β function through three loops. We also include in an appendix the result for several Abelian factors. We specialize to the case of the minimal supersymmetric standard model, and investigate the behavior of the Fayet-Iliopoulos coupling ξ for various boundary conditions at the unification scale. We focus particularly on the case of nonstandard soft supersymmetry breaking couplings, for which ξ evolves significantly between the unification scale and the weak scale.