Fayet-Iliopoulos D term and its renormalization in softly broken supersymmetric theories

We consider the renormalization of the Fayet-Iliopoulos D term in a softly broken Abelian supersymmetric theory, and calculate the associated β function through three loops. We show that there exists (at least through three loops) a renormalization group invariant trajectory for the coefficient of the D term, corresponding to the conformal anomaly solution for the soft masses and couplings.