The Operator Product Expansion Beyond Perturbation Theory in QCD

TL;DR

This paper reviews the Operator Product Expansion beyond perturbation theory in QCD and discusses its application in QCD sum rules for relating QCD to hadronic physics at various energies.

Contribution

It provides a concise overview of the OPE method beyond perturbation theory and illustrates recent applications in QCD sum rules for hadronic parameter determination.

Findings

QCD sum rules connect QCD with hadronic physics.

Applications include determining quark masses and strong coupling.

The method complements lattice QCD simulations.

Abstract

The Operator Product Expansion (OPE) of current correlators at short distances beyond perturbation theory in QCD, together with Cauchy's theorem in the complex energy plane, are the pillars of the method of QCD sum rules. This technique provides an analytic tool to relate QCD with hadronic physics at low and intermediate energies. It has been in use for over thirty years to determine hadronic parameters, form factors, and QCD parameters such as the quark masses, and the running strong coupling at the scale of the $\tau$-lepton. QCD sum rules provide a powerful complement to numerical simulations of QCD on the lattice. In this talk a short review of the method is presented for non experts, followed by three examples of recent applications.