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VOLUME 103 (2016) | ISSUE 2 | PAGE 83
Structure of three-loop contributions to the β-function of \boldsymbol{{\cal N}=1} SQED with Nf flavors, regularized by the dimensional reduction
DOI: 10.7868/S0370274X16020016
Abstract
In the case of using the higher derivative regularization for N=1 supersymmetric quantum electro-dynamics (SQED) with Nf flavors the loop integrals giving the β-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of the loop integrals to an integral of the δ-function and to derive the NSVZ relation for the renormalization group functions defined in terms of the bare coupling constant. In this paper we consider N=1 SQED with Nf flavors regularized by the dimensional reduction in the \overline{\mbox{DR}}-scheme. Evaluating the scheme-dependent three-loop contribution to the β-function proportional to (Nf)2 we find the structures analogous to integrals of the δ-singularities. After adding the scheme-independent terms proportional to (Nf)1 we obtain the known result for the three-loop β-function.