  We consider the short-distance expansion of the product of two gluon field
strength tensors connected by a straight-line-ordered Wilson line. The vacuum
expectation value of this nonlocal operator is a common object in studies of
the QCD vacuum structure, whereas its nucleon expectation value is known as the
gluon quasi-parton distribution and is receiving a lot of attention as a tool
to extract gluon distribution functions from lattice calculations. Extending
our previous study, we calculate the three-loop coefficient functions of the
scalar operators in the operator product expansion up to dimension four. As a
by-product, the three-loop anomalous dimension of the nonlocal two-gluon
operator is obtained as well.
