Structure of three-loop contributions to the β-function of N = 1 supersymmetric QED with Nf flavors regularized by the dimensional reduction

Abstract

In the case of using the higher derivative regularization for N = 1 supersymmetric quantum electrodynamics (SQED) with N_f flavors, the loop integrals giving the β-function are integrals of double total derivatives in themomentum space. This feature allows reducing one of the loop integrals to an integral of the δ-function and deriving the Novikov–Shifman–Vainshtein–Zakharov relation for the renormalization group functions defined in terms of the bare coupling constant. We consider N = 1 SQED with N_f flavors regularized by the dimensional reduction in the \(\overline {DR} \)-scheme. Evaluating the scheme-dependent three-loop contribution to the β-function proportional to (N_f)² we find the structures analogous to integrals of the δ-singularities. After adding the schemeindependent terms proportional to (N_f)¹, we obtain the known result for the three-loop β-function.