Verification of new identity for the Green functions in N=1 supersymmetric non-Abelian Yang--Mills theory with the matter fields

We investigate a new identity for Green functions using the higher covariant derivative regularization. It relates some coefficients in the vertex function of the matter superfield, in which one of external matter lines is not chiral. The calculation in the first nontrivial order (for the two-loop vertex function) reveals that the new identity is also valid for the non-Abelian Yang–Mills theory with matter fields. The new identity is shown to appear because three-loop integrals, defining the Gell-Mann–Low function are factorized into integrals of total derivatives.