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

**Authors**: A. L. Cherchiglia, M. Sampaio, B. Hiller, A. P. B. Scarpelli

**Ref.**: Eur. Phys. J. C **76(2)**, 47 (2016)

**Abstract**: 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.