Effective potential between two transverse gluons from lattice QCD

TL;DR

This paper derives an effective potential between two transverse gluons in glueballs from lattice QCD data, supporting the model of glueballs as bound states of gluons with a funnel-shaped interaction.

Contribution

It demonstrates that the effective gluon-gluon potential in glueballs can be extracted from lattice QCD results, revealing a funnel shape consistent with theoretical models.

Findings

The effective potential is compatible with a funnel shape.

A negative constant is needed to match the potential's height.

The potential may be influenced by instanton effects.

Abstract

Modeling glueballs as bound states of transverse constituent gluons allows to understand the main features of the lattice QCD glueball spectrum. In particular it has been shown in previous works that the lightest C-even glueballs can be seen as bound states of two transverse constituent gluons interacting via a funnel potential. In the present study we show that such an effective potential emerges from the available lattice QCD data. Starting from the scalar glueball mass and wave function computed in lattice QCD, we indeed compute the equivalent local potential between two transverse constituent gluons in the scalar channel and show that it is compatible with a funnel shape, where standard values of the parameters are used and where a negative constant has to be added to reproduce the absolute height of the potential. Such a constant could be related to instanton-induced effects in glueballs.