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

TL;DR

This paper calculates anomalous dimensions of four-quark operators in QCD and explores how these influence the infrared renormalon structure of mesonic two-point correlators, revealing more complex singularities than previously approximated.

Contribution

It provides the leading-order anomalous dimension matrices for four-quark operators and analyzes their impact on the infrared renormalon poles in full QCD.

Findings

Most singular pole has an exponent of approximately 3.2, indicating more complex singularity structure.

Compared to large-$eta_0$ approximation, full QCD shows higher-order poles.

Eigenvalues of anomalous dimension matrices significantly influence renormalon singularities.

Abstract

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 $\kappa\approx 3.2$.