Long-Range Forces of QCD

TL;DR

This paper investigates the long-range interactions between color dipoles in QCD, revealing a non-perturbative component that dominates at large distances and impacts scattering cross sections, with implications for heavy quarkonium physics.

Contribution

It derives the leading non-perturbative long-distance contribution to dipole interactions using low-energy QCD theorems and relates it to the QCD vacuum energy density.

Findings

Non-perturbative interaction decays as R^{-5/2} with exponential suppression.

In the heavy quark limit, non-perturbative effects diminish more slowly than perturbative ones.

Calculated cross sections for J/ and J/     scattering.

Abstract

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.