Abstract
It is known that factorization of the β-function loop integrals into integrals of double total derivatives is an important ingredient needed for deriving the NSVZ relation by direct perturbative calculations in \(\mathcal{N} = 1\) SQED regularized by thehigher derivatives. It allows to relate the β-function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant. In this work we find the analog of this result in the case of using dimensional reduction regularization in the lowest orders. However, we demonstrate that in this case the NSVZ relation is not satisfied for the RG functions defined in terms of the bare coupling constant. Nevertheless, it is possible to impose boundary conditions to the renormalization constants determining the NSVZ scheme in the three-loop order for the RG functions defined in terms of the renormalized coupling constant.
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ACKNOWLEDGMENTS
The author is grateful K.V. Stepanyantz and A.L. Kataev for the useful discussions and valuable remarks. This work was performed at Institute for Information Transmission Problems with the financial support of the Russian Science Foundation (Grant no. 14-50-00150).
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Aleshin, S.S. NSVZ Relation and the Dimensional Reduction in \(\mathcal{N}\) = 1 SQED. Phys. Part. Nuclei 49, 966–968 (2018). https://doi.org/10.1134/S1063779618050027
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DOI: https://doi.org/10.1134/S1063779618050027