Full numerical evaluation of the Cornell-potential Van der Waals interaction

Evaluate numerically the complete glueball-glueball Van der Waals potential derived from the Cornell colour interaction, including the required four-body wavefunctions and higher colour-representation intermediate states, in order to determine the interaction beyond the schematic Coulombic and approximate linear-potential treatments.

Background

The effective glueball-glueball interaction is obtained through a Feshbach reduction and depends on dipole matrix elements connecting two colour-singlet glueballs to intermediate pairs of coloured glueball states. A complete calculation therefore requires wavefunctions for the higher colour representations and their decomposition into two-body–two-body clusters within the four-gluon system.

The paper evaluates the Coulombic contribution in detail and treats the linear Cornell component schematically. A full numerical treatment would establish the quantitative size, range, and parameter dependence of the complete Cornell-induced Van der Waals interaction, especially because the Coulomb and linear contributions can substantially cancel for ground-state glueballs.

References

This requires solving a four-body problem where knowledge is more scarce particularly with regard to decomposing the states in two-body--two-body clusters in various colour representations. We will therefore postpone a full numerical evaluation of the result in Eq.~(\ref{ec:asintVdW}) to future work and content ourselves with getting an idea of its size for a Coulombic system, and later providing a very schematic treatment of the linear part in appendix~\ref{app:includelinear}.

— Glueball interactions from the colour Van der Waals potential  (2609.10841 - Cúneo et al., 9 Sep 2026) in Section "Longer and shorter range contributions with the Cornell potential", immediately before Subsection "1/R^3 longer-range tail"