Subtleties in the beta-function calculation of N=1 supersymmetric gauge theories

We investigate some peculiarities in the calculation of the two-loop beta function of N = 1 supersymmetric models which are intimately related to the so-called “anomaly puzzle”. There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, there is obtained a finite two-loop effective action, although a non-null coefficient for the beta function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly.