We consider the scattering of two color dipoles (e.g., heavy quarkonium
states) at low energy - a QCD analog of Van der Waals interaction. Even though
the couplings of the dipoles to the gluon field can be described in
perturbation theory, which leads to the potential proportional to
(N_c^2-1)/R^{7}, at large distances R the interaction becomes totally
non-perturbative. Low-energy QCD theorems are used to evaluate the leading
long-distance contribution \sim (N_f^2-1)/(11N_c - 2N_f)^2 R^{-5/2} exp(-2 \mu
R) (\mu is the Goldstone boson mass), which is shown to arise from the
correlated two-boson exchange. The sum rule which relates the overall strength
of the interaction to the energy density of QCD vacuum is derived.
Surprisingly, we find that when the size of the dipoles shrinks to zero (the
heavy quark limit in the case of quarkonia), the non-perturbative part of the
interaction vanishes more slowly than the perturbative part as a consequence of
scale anomaly. As an application, we evaluate elastic \pi J/\psi and \pi J/\psi
\to \pi \psi' cross sections.Comment: 16pages, 9 eps figures; discussion extended, 2 new references added,
to appear in Phys.Rev.
