Absence of the anomalous magnetic moment in a supersymmetric abelian gauge theory

We give a general argument for the vanishing of the anomalous magnetic moment in a supersymmetric Abelian gauge theory recently constructed by Wess and Zumino, provided in such a model the appropriate Ward identities are consistent with renormalized perturbation theory. Our conclusion is in fact confirmed by explicit one-loop calculation, thus providing a new example of cancellation of Feynman graphs in supersymmetric theories.