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We consider the general ${\cal N}=1$ supersymmetric gauge theory with matter,regularized by higher covariant derivatives without breaking the BRSTinvariance, in the massless limit. In the $\xi$-gauge we obtain the(unrenormalized) expression for the two-point Green function of the quantumgauge superfield in the one-loop approximation as a sum of integrals over theloop momentum. The result is presented as a sum of three parts: the first onecorresponds to the pure supersymmetric Yang--Mills theory in the Feynman gauge,the second one contains all gauge dependent terms, and the third one is thecontribution of diagrams with a matter loop. For the Feynman gauge and aspecial choice of the higher derivative regulator in the gauge fixing term weanalytically calculate these integrals in the limit $k\to 0$. In particular, inaddition to the leading logarithmically divergent terms, which are determinedby integrals of double total derivatives, we also find the finite constants.

One-loop polarization operator of the quantum gauge superfield for ${\cal N}=1$ SYM regularized by higher derivatives