Nonlocal gluon condensates in QCD sum rules

TL;DR

This paper develops a method to calculate nonlocal gluon condensates and their Wilson coefficients using the background field approach, enhancing the understanding of glueball correlators within QCD sum rules.

Contribution

It introduces a new calculation method for Wilson coefficients of nonlocal gluon condensates using Feynman diagrams in the background field approach, applied to glueball correlators.

Findings

Confirmed OPE results for two-gluon glueball correlators.

Calculated contributions from dimension-6 four-quark and dimension-8 mixed condensates.

Revisited three-gluon glueball OPEs up to dimension-6.

Abstract

Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. Short-distance expansions of two-, three-, and four-gluon condensates are presented up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators as examples. Methodological aspects of the background field approach are discussed in relation to glueball studies within QCD sum rules. We confirm the results for Operator Product Expansion (OPE) of the two-gluon $0^{\pm +}$ glueball current correlators and calculate additional contributions coming from dimension-6 four-quark condensate and dimension-8 mixed quark-gluon condensates. The OPEs used in QCD sum rules for three-gluon $0^{\pm +}$ glueballs are revisited up to dimension-6 order.