  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.
