Fayet-Iliopoulos D term and its renormalization in the minimal supersymmetric standard model - art. no. 075010

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 beta function through three l oops. We also include in an appendix the result for several Abelian factors . We specialize to the case of the minimal supersymmetric standard model, a nd investigate the behavior of the Fayet-Iliopoulos coupling xi for various boundary conditions at the unification scale. We focus particularly on the case of nonstandard soft supersymmetry breaking couplings, for which xi ev olves significantly between the unification scale and the weak scale.