Investigating the anomaly puzzle in N=1 supersymmetric electrodynamics

Using Schwinger-Dyson equations and Ward identities in the N=1 supersymmetric electrodynamics regularized by higher derivatives, we find that we can calculate some contributions to the two-point Green's function of the gauge field and to the β-function exactly in all orders of the perturbation theory. We use the results to investigate the anomaly puzzle in the considered theory.