  In this work, we calculate leading-order anomalous dimension matrices for
dimension-6 four-quark operators which appear in the operator product expansion
of flavour non-diagonal and diagonal vector and axial-vector two-point
correlation functions. The infrared renormalon structure corresponding to
four-quark operators is reviewed and it is investigated how the eigenvalues of
the anomalous dimension matrices influence the singular behaviour of the $u=3$
infrared renormalon pole. It is found that compared to the large-$\beta_0$
approximation where at most quadratic poles are present, in full QCD at $N_f=3$
the most singular pole is more than cubic with an exponent $\kappa\approx 3.2$.
