We consider the scattering of two color dipoles (e.g., heavy quarkonium states) at low energy—a QCD analogue 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 a potential proportional to ${(N}_c^2-{1)/R}^7,$ at large distances R the interaction becomes totally nonperturbative. Low-energy QCD theorems are used to evaluate the leading long-distance contribution $\sim {(N}_f^2-{1)/(11N}_c-{2N}_f{)}^2\hspace{0.5em}{R}^{-5/2}\exp \left(-2\mu R\right)$ $(\mu$ 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 the 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 nonperturbative part of the interaction vanishes more slowly than the perturbative part as a consequence of the scale anomaly. As an application, we evaluate elastic $\pi J/\psi$ and $\pi J/\overrightarrow{\psi }\pi {\psi }^{\prime }$ cross sections.

• Received 26 March 1999

DOI:https://doi.org/10.1103/PhysRevD.60.114039