Anomalous dimensions of four-quark operators and renormalon structure of mesonic two-point correlators

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 approximate to 3.2.