One-loop polarization operator of the quantum gauge superfield for 𝒩 = 1 SYM regularized by higher derivatives

Abstract

We consider the general [Formula: see text] supersymmetric gauge theory with matter, regularized by higher covariant derivatives without breaking the BRST invariance, in the massless limit. In the [Formula: see text]-gauge we obtain the (unrenormalized) expression for the two-point Green function of the quantum gauge superfield in the one-loop approximation as a sum of integrals over the loop momentum. The result is presented as a sum of three parts: the first one corresponds to the pure supersymmetric Yang–Mills theory in the Feynman gauge, the second one contains all gauge-dependent terms, and the third one is the contribution of diagrams with a matter loop. For the Feynman gauge and a special choice of the higher derivative regulator in the gauge fixing term, we analytically calculate these integrals in the limit [Formula: see text]. In particular, in addition to the leading logarithmically divergent terms, which are determined by integrals of double total derivatives, we also find the finite constants.