Structure of three-loop contributions to the

**β**-function of

SQED with

**N**_{f} flavors, regularized by the dimensional reduction

S. S. Aleshin^{+}, A. L. Kataev^{*}, K. V. Stepanyantz^{+}

^{+}Physical Faculty Lomonosov MSU, Department of Theoretical Physics, 119991 Moscow, Russia

^{*}Institute for Nuclear Research of the RAS, 117312 Moscow, Russia

**Abstract**
In the case of using the higher derivative
regularization for N=1 supersymmetric quantum electro-dynamics (SQED) with
N_{f} 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 N_{f} flavors regularized by the dimensional reduction in the
-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 scheme-independent terms proportional to (N_{f})^{1} we obtain the known
result for the three-loop β-function.