  We study the scattering of small color dipoles (e.g., heavy quarkonium
states) at low energies. We find that even though the couplings of color
dipoles to the gluon field can be described in perturbation theory, at large
distances the interaction becomes totally non--perturbative. The structure of
the scattering amplitude, however, is fixed by the (broken) chiral and scale
symmetries of QCD; the leading long--distance contribution arises from the
correlated two--pion exchange. We use the spectral representation technique to
evaluate both perturbative and non-perturbative contributions to the scattering
amplitude. Our main result is the sum rule which relates the overall strength
of the non--perturbative interaction between color dipoles to the energy
density of QCD vacuum.
