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, it 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.Comment: Few misprintings corrected and comments added. To meet the version to be published at European Physical Journal

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